A244003 - OEIS

%I #18 Jan 24 2019 16:15:02

%S 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 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 49,216,3125,65536,1594323,2097152,1,0

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

%H Alois P. Heinz, <a href="/A244003/b244003.txt">Antidiagonals n = 0..20, flattened</a>

%F A(n,k) = k^A000045(n).

%F A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.

%e Square array A(n,k) begins:

%e   1, 1,   1,    1,     1,      1,       1, ...

%e   0, 1,   2,    3,     4,      5,       6, ...

%e   0, 1,   2,    3,     4,      5,       6, ...

%e   0, 1,   4,    9,    16,     25,      36, ...

%e   0, 1,   8,   27,    64,    125,     216, ...

%e   0, 1,  32,  243,  1024,   3125,    7776, ...

%e   0, 1, 256, 6561, 65536, 390625, 1679616, ...

%p A:= (n, k)-> k^(<<1|1>, <1|0>>^n)[1, 2]:

%p seq(seq(A(n, d-n), n=0..d), d=0..12);

%t 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 Columns k=0-10 give: A000007, A000012, A000301, A010098, A010099, A214706, A215270, A214887, A215271, A215272, A010100.

%Y Rows n=0, 1+2, 3-8 give: A000012, A001477, A000290, A000578, A000584, A001016, A010801, A010809.

%Y Main diagonal gives: A152915.

%Y Cf. A000045, A103323.

%K nonn,tabl

%O 0,8

%A _Alois P. Heinz_, Jun 17 2014