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A250486 A(n,k) is the n^k-th Fibonacci number; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
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
Main diagonal gives A250495.
Cf. A000045.
Sequence in context: A068494 A200726 A195040 * A316826 A256449 A355340
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Nov 24 2014
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)