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A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals. 13
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

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.

EXAMPLE

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, ...

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-Fran├žois Alcover, Nov 11 2015 *)

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.

Sequence in context: A307432 A256140 A321391 * A332670 A118344 A119270

Adjacent sequences:  A244000 A244001 A244002 * A244004 A244005 A244006

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jun 17 2014

STATUS

approved

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)