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A244003
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A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.
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13
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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, 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, 49, 216, 3125, 65536, 1594323, 2097152, 1, 0
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OFFSET
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0,8
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LINKS
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FORMULA
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A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.
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EXAMPLE
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Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 1, 4, 9, 16, 25, 36, ...
0, 1, 8, 27, 64, 125, 216, ...
0, 1, 32, 243, 1024, 3125, 7776, ...
0, 1, 256, 6561, 65536, 390625, 1679616, ...
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MAPLE
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A:= (n, k)-> k^(<<1|1>, <1|0>>^n)[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..12);
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MATHEMATICA
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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 *)
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CROSSREFS
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Columns k=0-10 give: A000007, A000012, A000301, A010098, A010099, A214706, A215270, A214887, A215271, A215272, A010100.
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KEYWORD
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AUTHOR
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STATUS
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approved
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