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