A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 4, 3, 4, 1, 0, 1, 5, 4, 9, 8, 1, 0, 1, 6, 5, 16, 27, 32, 1, 0, 1, 7, 6, 25, 64, 243, 256, 1, 0, 1, 8, 7, 36, 125, 1024, 6561, 8192, 1, 0, 1, 9, 8, 49, 216, 3125, 65536, 1594323, 2097152, 1, 0

Offset: 0

Author

Alois P. Heinz, Jun 17 2014

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
  1, 1,   1,    1,     1,      1,       1, ...
  0, 1,   2,    3,     4,      5,       6, ...
  0, 1,   2,    3,     4,      5,       6, ...
  0, 1,   4,    9,    16,     25,      36, ...
  0, 1,   8,   27,    64,    125,     216, ...
  0, 1,  32,  243,  1024,   3125,    7776, ...
  0, 1, 256, 6561, 65536, 390625, 1679616, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..20, flattened

Crossrefs

Columns k=0-10 give: A000007, A000012, A000301, A010098, A010099, A214706, A215270, A214887, A215271, A215272, A010100.

Rows n=0, 1+2, 3-8 give: A000012, A001477, A000290, A000578, A000584, A001016, A010801, A010809.

Main diagonal gives: A152915.

Cf. A000045, A103323.

Programs

Maple

A:= (n, k)-> k^(<<1|1>, <1|0>>^n)[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..12);

Mathematica

A[0, 0] = 1; A[n_, k_] := k^Fibonacci[n]; Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 11 2015 *)

Formula

A(n,k) = k^A000045(n).

A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.