úÎ/E$RÉ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈ ÉÊËÌÍÎ     ] ,Your standard Co-Algebra (dual to Algebra). $An infinite Tree. Used to represent Streams A generating function for Streams. Your standard Streams , renamed to S because S looks like a meandering  stream.  !"#$%&'()*+,-./012345prepend, Hinze UFP p.3 6789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh$unzip, specialized to Stream tuples Ï p xs, removes any elements from xs that do not satisfy p. Beware6: this function may diverge if there is no element of  xs that satisfies p, e.g. filter odd (repeat 0) will loop. Ð p xs* returns the longest prefix of the stream  xs for which the predicate p holds. Ñ p xs$ returns the suffix remaining after  Ð p xs. Beware0: this function may diverge if every element of xs  satisfies p, e.g. dropWhile even (repeat 0) will loop.  p xs returns the longest prefix of xs that satisfies  p-, together with the remainder of the stream. The Ò p function is equivalent to Ó not . p. The Ô function takes an integer n and a stream xs 0 and returns a pair consisting of the prefix of xs of length  n= and the remaining stream immediately following this prefix. Beware8: passing a negative integer as the first argument will  cause an error. The  partition function takes a predicate p and a stream  xs>, and returns a pair of streams. The first stream corresponds  to the elements of xs for which p holds; the second stream  corresponds to the elements of xs for which p does not hold. Beware9: One of the elements of the tuple may be undefined. For  example, +fst (partition even (repeat 0)) == repeat 0 ; on the  other hand snd (partition even (repeat 0)) is undefined. The 1 function takes a stream and returns a stream of A lists such that flattening the resulting stream is equal to the ; argument. Moreover, each sublist in the resulting stream - contains only equal elements. For example, Õ n xs drops the first n elements off the front of  the sequence xs. Beware8: passing a negative integer as the first argument will  cause an error. The stails function takes a stream xs and returns all the  suffixes of xs. Amerge, version 2 [Hinze UFP p.35] map, version 1  | map, version 2  | map2, really zip? from Unique Fixed Point p.35 union for streams Interleave two Streams xs and ys, alternating elements  from each list. ; [x1,x2,...] `interleave` [y1,y2,...] == [x1,y1,x2,y2,...] 4 y xs" creates an alternating stream of  elements from xs and y. infix prepend turn something Ö xs$ returns the infinite repetition of xs: < cycle [1,2,3] = Cons 1 (Cons 2 (Cons 3 (Cons 1 (Cons 2 ... Arithmatic, Jumping, ... multiplication  | stream inversion  | finite (forward) difference $ | duplicate the head of the stream  | even (indexed) elements  | odd (indexed) elements  | even (indexed) elements, v2  | odd (indexed) elements, v2 ' | drop function, results in (4*n - 1) # | drop function, results in (2*n)  | an alternative tail function a kind of sum function  | right inverse of diff from Hinze UFP p.45 from Hinze UFP p.49 from Hinze UFP p.4 $iterate (inductively) over a stream this can't be stopped? from Hinze UFP p.39 from Hinze UFP p.41  2D operator? from Hinze UFP p.45 from Hinze UFP p.45 mutually recursive from Hinze UFP p.45 from Hinze UFP p.45 A scan f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...] scan' is a strict scan. G is a variant of E& that has no starting value argument: / scan1 f [x1, x2, ...] == [x1, x1 `f` x2, ...] scan1'. is a strict scan that has no starting value. I4 computes the transposition of a stream of streams. from Hinze UFP p.45 from Hinze UFP p.45 standard fix-point function J | standard fix-point function, specialized to Streams (forward ordering) J | standard fix-point function, specialized to Streams (reverse ordering) +transform a generator to a Stream operator 4 | transform a generator to a Stream operator - v2? . | transform a Stream operator to a generator M | transform a generator, along with a reversed list, into a Stream operator "smart constructor for Tree labels ' | smart constructor for Tree branches # | translate a Tree to a Generator # | translate a Generator to a Tree 0 | translate a Tree element to a Stream element 5 | translate a Generator element to a Stream element " | fromFG helper function (head) ! | fromFG helper function (tail) K | fromRG: translate a Generator (and a reversed list) to a Stream element ! | fromRG helper function (head) ! | fromRG helper function (tail) ,unfold operator, specialized to Co-Algebras ; | standard fix-point function, specialized to Co-Algebras 2 | generate a Stream operator, given a Co-Algebra ,utility function to lookup sequence in OEIS A | utility function to check of all elements of a list are equal 3 | utility function to unwrap a (known good) Maybe < | utility function to map over adjacent elements in a list  Power Series Glasses Horner's Rule on Streams 's = sconst (shead t) + (z |*| stail s) implies  z |*| s = 0 <|| s ]  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh]5$#!g;<=8@f:.01/aKJ?%()bL34&c6[NQMO]^RP_`\YX WZV STU'*+,CADBEFGH7> 9"-2Iedh]  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghprobably portable  experimental drewday@gmail.com `istake 30 $ sZero=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]jstake 30 $ fwdFix gZero=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]kstake 30 $ revFix rZero=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]lstake 30 $ cZero=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]mno$Believe it or not, this is in OEIS: take 30 $ fromOEIS "A000012"=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]stake 30 $ sOne=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]pstake 30 $ sOnes=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]qrstake 30 $ fwdFix gOne=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]sstake 30 $ revFix rOne=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]tstake 30 $ cOne=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]uvwtake 30 $ fromOEIS "A000027"R[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]stake 30 $ sNatQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]xstake 30 $ siterate (+1) 0Q[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]ystake 30 $ natnatQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]z{stake 30 $ fwdFix gNatQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]|stake 30 $ revFix rNatQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]}stake 30 $ cNatQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]~€stake 30 $ binQ[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]take 15 $ fromOEIS "A122803"8[1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384]stake 15 $ revPowersOfN2?[1,-2,4,-8,16,-32,64,-128,256,-512,1024,-2048,4096,-8192,16384]‚ƒstake 15 $ potW[True,True,False,True,False,False,False,True,False,False,False,False,False,False,False]„take 15 $ fromOEIS "A000244"I[1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,4782969]stake 15 $ revPowersOf3I[1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,4782969]…†take 30 $ fromOEIS "A000290"k[0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841]stake 30 $ bsum $ 2 * sNat + 1k[0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841]‡take 10 $ fromOEIS "A000142"&[1,1,2,6,24,120,720,5040,40320,362880]stake 10 $ sFac&[1,1,2,6,24,120,720,5040,40320,362880]ˆtake 29 $ fromOEIS "A000045"y[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]stake 29 $ sFiby[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]‰stake 29 $ sFib2y[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]Šstake 29 $ revFix revGfibsy[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]‹Œstake 29 $ cFiby[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]Žstake 29 $ fwdFix gFibsy[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811]take 28 $ fromOEIS "A000032"{[2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39603,64079,103682,167761,271443,439204]stake 28 $ sLucas{[2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39603,64079,103682,167761,271443,439204]stake 28 $ revFix rLucas{[2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39603,64079,103682,167761,271443,439204]‘3The Fibionacci (4n + 1) and Lucas (4n + 1) numbers ,drop0L is evidently a bisect twice function stake 10 $ drop0L sFib5[1,5,34,233,1597,10946,75025,514229,3524578,24157817]take 10 $ fromOEIS "A033889"5[1,5,34,233,1597,10946,75025,514229,3524578,24157817]’stake 10 $ drop0L sLucas8[1,11,76,521,3571,24476,167761,1149851,7881196,54018521]take 10 $ fromOEIS "A056914"8[1,11,76,521,3571,24476,167761,1149851,7881196,54018521]“&The Fib (2*n) and Lucas (2*n) numbers (dromIp1L is evidently a bisect function stake 20 $ dropIp1L sFibh[0,1,3,8,21,55,144,377,987,2584,6765,17711,46368,121393,317811,832040,2178309,5702887,14930352,39088169]take 20 $ fromOEIS "A001906"h[0,1,3,8,21,55,144,377,987,2584,6765,17711,46368,121393,317811,832040,2178309,5702887,14930352,39088169]”stake 20 $ dropIp1L sLucaso[2,3,7,18,47,123,322,843,2207,5778,15127,39603,103682,271443,710647,1860498,4870847,12752043,33385282,87403803]take 20 $ fromOEIS "A005248"o[2,3,7,18,47,123,322,843,2207,5778,15127,39603,103682,271443,710647,1860498,4870847,12752043,33385282,87403803]•!stake 21 $ [1] <<| plus sFib sFibI[1,0,2,2,4,6,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362]take 21 $ fromOEIS "A006355"I[1,0,2,2,4,6,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362]–take 20 $ fromOEIS "A039834";[1,1,0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597]stake 20 $ [1] <<| diff sFib;[1,1,0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597]—take 20 $ fromOEIS "A061084"D[1,2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778]stake 20 $ diff sLucasE[-1,2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778]˜take 30 $ fromOEIS "A000931"S[1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616]stake 30 $ padovanPP11010S[1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616]™take 30 $ fromOEIS "A134816"a[1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616,816,1081,1432,1897,2513]stake 30 $ padovana[1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616,816,1081,1432,1897,2513]šstake 30 $ revFix rpadovana[1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465,616,816,1081,1432,1897,2513]›take 31 $ fromOEIS "A133034"O[1,0,1,1,1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265](stake 30 $ diff $ diff $ revFix rpadovanN[0,1,-1,1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265]œtake 30 $ fromOEIS "A001608"e[3,0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486,644,853,1130,1497,1983,2627,3480]stake 30 $ perrine[3,0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486,644,853,1130,1497,1983,2627,3480]stake 30 $ revFix rperrine[3,0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486,644,853,1130,1497,1983,2627,3480]žGenerating Function: z  --------------------  z^2 + 2z - 1 take 20 $ fromOEIS "A000129"`[0,1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,1136689,2744210,6625109]Ÿ stake 20 $ cPell`[0,1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,1136689,2744210,6625109]¡stake 20 $ revFix rpell`[0,1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,1136689,2744210,6625109]¢take 20 $ fromOEIS "A001045"Q[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763]stake 20 $ jacobQ[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763]£stake 20 $ revFix rjacobQ[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763]¤take 20 $ fromOEIS "A014551"Y[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287]stake 20 $ jacoblY[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287]¥stake 20 $ revFix rjacoblY[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287]¦%take 30 $ drop 1 $ fromOEIS "A006257"J[1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29]stake 30 $ josJ[1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29]§stake 30 $ josAltJ[1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29]¨%take 30 $ drop 1 $ fromOEIS "A053644"L[1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16]stake 30 $ msbL[1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16]©take 30 $ fromOEIS "A010060"=[0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0]stake 30 $ athue=[0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0]ª«stake 30 $ thue=[0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0]¬stake 30 $ binlike1=[0,1,0,1,2,0,0,1,2,2,4,0,0,0,0,1,2,2,4,2,4,4,8,0,0,0,0,0,0,0]­stake 30 $ binlike2=[0,1,1,0,1,2,0,2,1,0,2,2,0,4,2,0,1,4,0,2,2,0,2,4,0,4,4,0,2,8]®take 30 $ fromOEIS "A000035"=[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]stake 30 $ bsum 0 |~| 1=[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]¯take 30 $ fromOEIS "A011371"O[0,0,1,1,3,3,4,4,7,7,8,8,10,10,11,11,15,15,16,16,18,18,19,19,22,22,23,23,25,25]stake 30 $ sumcarryO[0,0,1,1,3,3,4,4,7,7,8,8,10,10,11,11,15,15,16,16,18,18,19,19,22,22,23,23,25,25]°take 20 $ fromOEIS "A060790"k[1,2,2,3,15,38,110,323,927,2682,7754,22403,64751,187134,540822,1563011,4517183,13054898,37729362,109039875]stake 20 $ revFix apolloD2Ÿ[2.0,2.0,3.0,15.0,38.0,110.0,323.0,927.0,2682.0,7754.0,22403.0,64751.0,187134.0,540822.0,1563011.0,4517183.0,1.3054898e7,3.7729362e7,1.09039875e8,3.15131087e8]±stake 20 $ revFix apolloD2altV[2.0,2.0,3.0,-1.0,2.0,2.0,3.0,-1.0,2.0,2.0,3.0,-1.0,2.0,2.0,3.0,-1.0,2.0,2.0,3.0,-1.0]²³´µ¶stake 32 $ streamApD3k[0,0,1,1,1,2,2,3,4,8,9,9,15,32,32,33,56,120,121,121,209,450,450,451,780,1680,1681,1681,2911,6272,6272,6273]·stake 4 $ streamApD3's[(0,0,1,1,1,2,2,3),(4,8,9,9,15,32,32,33),(56,120,121,121,209,450,450,451),(780,1680,1681,1681,2911,6272,6272,6273)]¸take 30 $ fromOEIS "A025480"B[0,0,1,0,2,1,3,0,4,2,5,1,6,3,7,0,8,4,9,2,10,5,11,1,12,6,13,3,14,7]stake 30 $ fracB[0,0,1,0,2,1,3,0,4,2,5,1,6,3,7,0,8,4,9,2,10,5,11,1,12,6,13,3,14,7]¹take 30 $ fromOEIS "A000265"J[1,1,3,1,5,3,7,1,9,5,11,3,13,7,15,1,17,9,19,5,21,11,23,3,25,13,27,7,29,15]stake 30 $ godJ[1,1,3,1,5,3,7,1,9,5,11,3,13,7,15,1,17,9,19,5,21,11,23,3,25,13,27,7,29,15]º  diverges!!»take 30 $ fromOEIS "A051037"S[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,36,40,45,48,50,54,60,64,72,75,80]stake 30 $ hammingS[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,36,40,45,48,50,54,60,64,72,75,80]¼½take 30 $ fromOEIS "A092323"L[0,1,1,3,3,3,3,7,7,7,7,7,7,7,7,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15]stake 30 $ (diff sNat - msb)i[0,-1,-1,-3,-3,-3,-3,-7,-7,-7,-7,-7,-7,-7,-7,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15,-15]¾take 30 $ fromOEIS "A007814"=[0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1]stake 30 $ carry=[0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1]¿FIXME : Incorrect! Àstake 30 $ tree 0=[0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1]Átake 30 $ fromOEIS "A004526"G[0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14]stake 30 $ a004526G[0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14] take 16 $ 0 : fromOEIS "A000330"6[0,0,1,5,14,30,55,91,140,204,285,385,506,650,819,1015]stake 16 $ a0003306[0,0,1,5,14,30,55,91,140,204,285,385,506,650,819,1015]à take 21 $ 1 : fromOEIS "A078008"S[1,1,0,2,2,6,10,22,42,86,170,342,682,1366,2730,5462,10922,21846,43690,87382,174762]ÄÅstake 21 $ [1,1] <<| iterk2nkS[1,1,0,2,2,6,10,22,42,86,170,342,682,1366,2730,5462,10922,21846,43690,87382,174762]Ætake 15 $ fromOEIS "A090017"S[0,1,4,18,80,356,1584,7048,31360,139536,620864,2762528,12291840,54692416,243353344]stake 15 $ revFix a090017S[0,1,4,18,80,356,1584,7048,31360,139536,620864,2762528,12291840,54692416,243353344]Çtake 15 $ fromOEIS "A085449"C[0,1,2,8,24,80,256,832,2688,8704,28160,91136,294912,954368,3088384]stake 15 $ revFix horadam0142C[0,1,2,8,24,80,256,832,2688,8704,28160,91136,294912,954368,3088384]Ètake 15 $ fromOEIS "A002605"?[0,1,2,6,16,44,120,328,896,2448,6688,18272,49920,136384,372608]stake 15 $ revFix a002605?[0,1,2,6,16,44,120,328,896,2448,6688,18272,49920,136384,372608]`ijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈ`ijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈ`ijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈ×      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÎÏÑÎÒÓÎÏÔÎÏÕÎÏÖÎרÎ×ÙÎ×ÚÎ×ÛÎ×ÜÎ×ÝÎ×ÞÎ×ßà rivers-0.1.0Data.Rivers.NumExtData.Rivers.IdiomData.Rivers.StreamsData.Rivers.EcologyNumExt/^factfallchooseIdiompuresrepeat<>smapzipCoalgTreeNodeGSConssunzipsfilter stakeWhile sdropWhilesspansbreakssplitAt spartitiongroupsdropinitstails<||sheadstailanyAstakeago|~||!|map1sMapmergeunionsMap2sMap3sMap4smergeplus alternate interleave interleave'szipWith interleave3 intersperse<<|turnscycledifftail2timesasumbsumcsumsiteratedupinvsevensoddsEvensOddscanscan'scan1scan1' transposedropIp1Ldrop0LfixfwdFixrevFixgrowrgen'rgenrepunfoldcfixgroWlabelbranchestoGtoTfromTfromFGfromRGhOfFGtOfFGhOfRGtOfRG combStreamsallEqual mapAdjacentfromOEISfromJustsconstz0mainsZerogZerorZerocZerocZeroHcZeroTsOnesOnesgOnegOne'rOnecOnecOneHcOneTsNatsNatItnatnatgNatgNat'rNatcNatcNatHcNatTbin revPowersOfN2a122803pot revPowersOf3pothreea000290sFacsFibsFib2revGfibscFibcFibHcFibTgFibssLucasrLucasfib4np1luc4np1fib2nluc2nfibpfibdxFibdxLucaspadovanPP11010padovanrpadovan d2xpadovanperrinrperrincPellcPellHcPellTrpelljacobrjacobjacoblrjacobljosjosAltmsbathuethuethue'binlike1binlike2lsbsumcarryapolloD2 apolloD2altapd2frapd3proy streamApD3 streamApD3'fracgodblahhammingmontesta092323carryaltCarrytreea004526a000330iterk2nk iterk2nkH iterk2nkTa090017 horadam0142a002605baseGHC.RealRatioRational Data.RatioapproxRational denominator numerator%GHC.Listfilter takeWhile dropWhilebreakspansplitAtdropcycle