A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.
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
Offset: 0
Examples
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, ...
Links
- Alois P. Heinz, Antidiagonals n = 0..20, flattened
Crossrefs
Programs
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Maple
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
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 *)
Formula
A(n,k) = k^A000045(n).
A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.