A250486 A(n,k) is the n^k-th Fibonacci number; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 2, 1, 0, 1, 21, 34, 3, 1, 0, 1, 987, 196418, 987, 5, 1, 0, 1, 2178309, 37889062373143906, 10610209857723, 75025, 8, 1

Offset

0,13

Links

Alois P. Heinz, Antidiagonals n = 0..10, flattened

Wikipedia, Fibonacci number

Formula

A(n,k) = [0, 1; 1, 1]^(n^k)[1,2].

Example

Square array A(n,k) begins:
  1,  0,  0,      0,       0,    0,  0,  0,   ...
  1,  1,  1,      1,       1,    1,  1,  1,   ...
  1,  1,  3,      21,      987,  2178309,     ...
  1,  2,  34,     196418,  37889062373143906, ...
  1,  3,  987,    10610209857723,             ...
  1,  5,  75025,  59425114757512643212875125, ...
  1,  8,  14930352,                           ...
  1,  13, 7778742049,                         ...

Maple

A:= (n, k)-> (<<0|1>, <1|1>>^(n^k))[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..8);

Mathematica

A[n_, k_] := MatrixPower[{{0, 1}, {1, 1}}, n^k][[1, 2]]; A[0, 0] = 1;
Table[A[n, d-n], {d, 0, 8}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 28 2019, from Maple *)

Crossrefs

Columns k=0-8 give: A000012, A000045, A054783, A182149, A250490, A250491, A250492, A250493, A250494.

Rows n=0-10 give: A000007, A000012, A058635, A045529, A145231, A145232, A145233, A145234, A250487, A250488, A250489.

Main diagonal gives A250495.

Cf. A000045.

Sequence in context: A068494 A200726 A195040 * A316826 A256449 A355340

Adjacent sequences: A250483 A250484 A250485 * A250487 A250488 A250489

Keyword

nonn,tabl

Author

Alois P. Heinz, Nov 24 2014

Status

approved