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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 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

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