cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A321428 Expansion of Product_{i>0, j>0} (1 + x^(i^2 + j^2)).

Original entry on oeis.org

1, 0, 1, 0, 0, 2, 0, 2, 1, 0, 4, 0, 3, 4, 0, 8, 0, 6, 8, 2, 13, 2, 9, 14, 4, 22, 8, 16, 24, 8, 35, 18, 28, 38, 19, 52, 34, 46, 60, 40, 78, 58, 76, 94, 75, 120, 93, 124, 140, 126, 183, 150, 200, 210, 204, 276, 239, 308, 319, 316, 417, 366, 465, 480, 484, 620, 554
Offset: 0

Views

Author

Seiichi Manyama, Nov 09 2018

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 100; A063725 = Rest[CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/4, {x, 0, nmax}], x]]; s = 1; Do[s *= Sum[Binomial[A063725[[k]], j]*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]];, {k, 2, nmax}]; Take[CoefficientList[s, x], nmax + 1] (* Vaclav Kotesovec, Nov 09 2018 *)

Formula

G.f.: Product_{k>0} (1 + x^k)^A063725(k).

A321432 Expansion of Product_{i>0, j>0, k>0} (1 - x^(i^2 + j^2 + k^2)).

Original entry on oeis.org

1, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, -3, 5, 0, -3, 7, 0, 12, -7, -3, 21, -14, 3, -6, 6, 27, -57, 22, 6, -36, 15, -75, 87, -17, -111, 99, -71, 75, -90, -91, 324, -225, 23, 57, -36, 332, -543, 333, 374, -417, 342, -473, 720, 18, -1132, 1227, -330, 202, -414, -846, 2357, -1998
Offset: 0

Views

Author

Seiichi Manyama, Nov 09 2018

Keywords

Crossrefs

Formula

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

A321433 Expansion of Product_{i>0, j>0, k>0} 1/(1 - x^(i^2 + j^2 + k^2)).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 4, 0, 0, 7, 0, 3, 14, 0, 9, 23, 0, 21, 45, 3, 48, 72, 12, 96, 124, 39, 180, 204, 105, 327, 343, 225, 585, 572, 468, 1011, 976, 903, 1719, 1662, 1689, 2895, 2844, 3018, 4836, 4791, 5355, 8013, 8061, 9234, 13182, 13429, 15714, 21573, 22257, 26346
Offset: 0

Views

Author

Seiichi Manyama, Nov 09 2018

Keywords

Crossrefs

Convolution inverse of A321432.

Formula

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

A321457 Expansion of Product_{1 <= i <= j <= k} (1 + x^(i^2 + j^2 + k^2)).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 3, 3, 1, 4, 4, 2, 5, 4, 3, 7, 7, 5, 9, 10, 7, 11, 14, 9, 15, 19, 12, 22, 23, 17, 30, 29, 23, 41, 37, 32, 54, 46, 45, 68, 59, 63, 85, 79, 85, 107, 103, 108, 136, 136, 139, 174, 177, 178, 222, 225, 226, 287, 282, 290
Offset: 0

Views

Author

Seiichi Manyama, Nov 10 2018

Keywords

Crossrefs

Formula

G.f.: Product_{k>0} (1 + x^k)^A025427(k).
Showing 1-4 of 4 results.