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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.

%I A250486 #21 May 28 2019 08:10:57
%S A250486 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,
%T A250486 1,2178309,37889062373143906,10610209857723,75025,8,1
%N A250486 A(n,k) is the n^k-th Fibonacci number; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H A250486 Alois P. Heinz, <a href="/A250486/b250486.txt">Antidiagonals n = 0..10, flattened</a>
%H A250486 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number</a>
%F A250486 A(n,k) = [0, 1; 1, 1]^(n^k)[1,2].
%e A250486 Square array A(n,k) begins:
%e A250486   1,  0,  0,      0,       0,    0,  0,  0,   ...
%e A250486   1,  1,  1,      1,       1,    1,  1,  1,   ...
%e A250486   1,  1,  3,      21,      987,  2178309,     ...
%e A250486   1,  2,  34,     196418,  37889062373143906, ...
%e A250486   1,  3,  987,    10610209857723,             ...
%e A250486   1,  5,  75025,  59425114757512643212875125, ...
%e A250486   1,  8,  14930352,                           ...
%e A250486   1,  13, 7778742049,                         ...
%p A250486 A:= (n, k)-> (<<0|1>, <1|1>>^(n^k))[1, 2]:
%p A250486 seq(seq(A(n, d-n), n=0..d), d=0..8);
%t A250486 A[n_, k_] := MatrixPower[{{0, 1}, {1, 1}}, n^k][[1, 2]]; A[0, 0] = 1;
%t A250486 Table[A[n, d-n], {d, 0, 8}, {n, 0, d}] // Flatten (* _Jean-François Alcover_, May 28 2019, from Maple *)
%Y A250486 Columns k=0-8 give: A000012, A000045, A054783, A182149, A250490, A250491, A250492, A250493, A250494.
%Y A250486 Rows n=0-10 give: A000007, A000012, A058635, A045529, A145231, A145232, A145233, A145234, A250487, A250488, A250489.
%Y A250486 Main diagonal gives A250495.
%Y A250486 Cf. A000045.
%K A250486 nonn,tabl
%O A250486 0,13
%A A250486 _Alois P. Heinz_, Nov 24 2014