A321436 Expansion of Product_{1 <= i <= j} (1 - x^(i^2 + j^2)).

1, 0, -1, 0, 0, -1, 0, 1, -1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 1, 1, -2, 1, 2, 0, -1, 0, -1, 0, 2, -2, 1, 1, -4, 0, 3, -1, -1, 3, -2, -1, 0, -4, 5, 2, -3, 2, 3, -5, -3, 6, -3, -1, 0, -2, 1, 1, 0, 2, 7, -7, 0, 7, -9, -2, 4, -3, 2, 6, -9, 2, 12, -12, 1, 9, -11, -3, 7, 0, -1, 5

Offset: 0

Author

Seiichi Manyama, Nov 09 2018

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A025426, A321430, A321435, A321437.

Programs

Maple

N:= 100: # for a(1)..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

Formula

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