OFFSET
0,8
COMMENTS
A(n,k) is the number of ways of writing n as a sum of k square pyramidal numbers (A000330).
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
Eric Weisstein's World of Mathematics, Square Pyramidal Number
FORMULA
G.f. of column k: (Sum_{j>=0} x^(j*(j+1)*(2*j+1)/6))^k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 0, 1, 3, 6, 10, ...
0, 0, 0, 1, 4, 10, ...
0, 0, 0, 0, 1, 5, ...
0, 1, 2, 3, 4, 6, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Sum[x^(i (i + 1) (2 i + 1)/6), {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 13}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Jul 31 2017
STATUS
approved