A321423 -id:A321423 - cp's OEIS frontend

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

Seiichi Manyama, Nov 09 2018

nonn

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

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

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

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

A321424 Expansion of 1/2 * Product_{0 <= i <= j <= k} (1 + x^(i^2 + j^2 + k^2)).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 4, 5, 8, 9, 11, 14, 16, 21, 25, 28, 35, 43, 50, 60, 70, 82, 98, 113, 131, 155, 182, 210, 244, 283, 326, 377, 432, 495, 571, 657, 747, 856, 979, 1112, 1269, 1439, 1632, 1859, 2105, 2377, 2694, 3040, 3426, 3867, 4349, 4894, 5509, 6184, 6939, 7788

Offset: 0

Seiichi Manyama, Nov 09 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000164, A321381, A321423.

G.f.: Product_{k>0} (1 + x^k)^A000164(k).

cp's OEIS Frontend

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

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