OFFSET
0,13
LINKS
Alois P. Heinz, Antidiagonals n = 0..10, flattened
Wikipedia, Fibonacci number
FORMULA
A(n,k) = [0, 1; 1, 1]^(n^k)[1,2].
EXAMPLE
Square array A(n,k) begins:
1, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 3, 21, 987, 2178309, ...
1, 2, 34, 196418, 37889062373143906, ...
1, 3, 987, 10610209857723, ...
1, 5, 75025, 59425114757512643212875125, ...
1, 8, 14930352, ...
1, 13, 7778742049, ...
MAPLE
A:= (n, k)-> (<<0|1>, <1|1>>^(n^k))[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..8);
MATHEMATICA
A[n_, k_] := MatrixPower[{{0, 1}, {1, 1}}, n^k][[1, 2]]; A[0, 0] = 1;
Table[A[n, d-n], {d, 0, 8}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 28 2019, from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Nov 24 2014
STATUS
approved