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A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.

%I A244003 #18 Jan 24 2019 16:15:02
%S A244003 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,
%T A244003 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,
%U A244003 49,216,3125,65536,1594323,2097152,1,0
%N A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H A244003 Alois P. Heinz, <a href="/A244003/b244003.txt">Antidiagonals n = 0..20, flattened</a>
%F A244003 A(n,k) = k^A000045(n).
%F A244003 A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.
%e A244003 Square array A(n,k) begins:
%e A244003   1, 1,   1,    1,     1,      1,       1, ...
%e A244003   0, 1,   2,    3,     4,      5,       6, ...
%e A244003   0, 1,   2,    3,     4,      5,       6, ...
%e A244003   0, 1,   4,    9,    16,     25,      36, ...
%e A244003   0, 1,   8,   27,    64,    125,     216, ...
%e A244003   0, 1,  32,  243,  1024,   3125,    7776, ...
%e A244003   0, 1, 256, 6561, 65536, 390625, 1679616, ...
%p A244003 A:= (n, k)-> k^(<<1|1>, <1|0>>^n)[1, 2]:
%p A244003 seq(seq(A(n, d-n), n=0..d), d=0..12);
%t A244003 A[0, 0] = 1; A[n_, k_] := k^Fibonacci[n]; Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Nov 11 2015 *)
%Y A244003 Columns k=0-10 give: A000007, A000012, A000301, A010098, A010099, A214706, A215270, A214887, A215271, A215272, A010100.
%Y A244003 Rows n=0, 1+2, 3-8 give: A000012, A001477, A000290, A000578, A000584, A001016, A010801, A010809.
%Y A244003 Main diagonal gives: A152915.
%Y A244003 Cf. A000045, A103323.
%K A244003 nonn,tabl
%O A244003 0,8
%A A244003 _Alois P. Heinz_, Jun 17 2014