A321435 Expansion of Product_{1 <= i <= j} (1 + x^(i^2 + j^2)).

1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 2, 0, 3, 0, 2, 3, 1, 4, 1, 2, 4, 1, 6, 3, 4, 6, 2, 7, 5, 6, 8, 5, 9, 7, 9, 10, 9, 12, 10, 13, 14, 13, 18, 13, 19, 17, 18, 25, 19, 28, 24, 25, 33, 26, 36, 35, 33, 46, 35, 47, 48, 44, 61, 48, 62, 65, 60, 78, 68, 79, 87, 79, 101, 93

Offset

0,11

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>0} (1 + x^k)^A025426(k).

Maple

N:= 100: # for a(0)..a(N)
P:= 1:
for i from 1 to floor(sqrt(N)) do
  for j from i while i^2 + j^2 <= N do
    P:= P * (1 + x^(i^2 + j^2))
od od:
S:= series(P, x, N+1):
seq(coeff(S, x, k), k=0..N); # Robert Israel, Apr 21 2024

Crossrefs

Cf. A025426, A321423, A321428, A321436, A321437.

Sequence in context: A113408 A242653 A191530 * A173863 A022337 A025687

Adjacent sequences: A321432 A321433 A321434 * A321436 A321437 A321438

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2018

Status

approved