A321381 -id:A321381 - cp's OEIS frontend

A321429 Expansion of Product_{i>0, j>0, k>0} (1 + x^(i^2 + j^2 + k^2)).

1, 0, 0, 1, 0, 0, 3, 0, 0, 6, 0, 3, 7, 0, 9, 13, 0, 18, 19, 3, 39, 28, 9, 66, 42, 33, 105, 68, 78, 168, 111, 153, 261, 185, 285, 411, 325, 483, 636, 563, 798, 1017, 949, 1275, 1620, 1556, 2061, 2547, 2500, 3303, 4008, 3969, 5226, 6216, 6252, 8301, 9534, 9784, 12984

Offset: 0

Seiichi Manyama, Nov 09 2018

nonn

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

Cf. A063691, A321381, A321428.

G.f.: Product_{k>0} (1 + x^k)^A063691(k).

A321380 Expansion of 1/2 * Product_{i>=0, j>=0} (1 + x^(i^2 + j^2)).

Original entry on oeis.org

1, 2, 2, 2, 3, 6, 8, 8, 8, 12, 19, 22, 22, 26, 37, 48, 53, 58, 72, 92, 108, 118, 136, 166, 195, 222, 254, 298, 346, 394, 453, 524, 600, 672, 762, 884, 1011, 1126, 1255, 1438, 1652, 1850, 2047, 2302, 2626, 2960, 3274, 3636, 4095, 4602, 5112, 5662, 6319, 7056, 7834

Offset: 0

Seiichi Manyama, Nov 08 2018

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A000925, A033461, A321381.

G.f.: Product_{k>0} (1 + x^k)^A000925(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

A321429 Expansion of Product_{i>0, j>0, k>0} (1 + x^(i^2 + j^2 + k^2)).

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A321380 Expansion of 1/2 * Product_{i>=0, j>=0} (1 + x^(i^2 + j^2)).

Views

Author

Keywords

Links

Crossrefs

Formula

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

Views

Author

Keywords

Links

Crossrefs

Formula