def m := 3

def A :=
  generateTensor
    (\x y -> match (x, y) as (integer, integer) with
      | (#1, _) -> 1
      | ($x, #(x - 1)) -> 1
      | (_, _) -> 0)
    [m, m]

A
-- [| [| 1, 1, 1 |], [| 1, 0, 0 |], [| 0, 1, 0 |] |]

def B :=
  generateTensor
    (\x -> if x = 1 then 1 else 0)
    [m]

B
-- [| 1, 0, 0 |]

M.* A B
--[| 1, 1, 0 |]

M.* (M.power A 2) B
--[| 2, 1, 1 |]

M.* (M.power A 3) B
--[| 4, 2, 1 |]

M.* (M.power A 4) B
--[| 7, 4, 2 |]

M.* (M.power A 5) B
--[| 13, 7, 4 |]

M.* (M.power A 100) B
--[| 180396380815100901214157639, 98079530178586034536500564, 53324762928098149064722658 |]