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 1-2 of 2 results.

A363904 Expansion of Sum_{k>0} x^(3*k) / (1 - x^(4*k))^2.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 1, 0, 2, 5, 0, 0, 1, 5, 0, 3, 3, 6, 1, 0, 0, 8, 2, 0, 5, 8, 0, 4, 0, 11, 1, 0, 5, 11, 0, 0, 3, 11, 3, 5, 6, 12, 1, 2, 0, 14, 0, 0, 8, 17, 2, 6, 0, 15, 5, 0, 8, 19, 0, 0, 4, 17, 0, 7, 11, 18, 1, 0, 0, 24, 5, 5, 11, 20, 0, 8, 0, 21, 3, 0, 11, 23, 3, 0, 5, 25, 6
Offset: 1

Views

Author

Seiichi Manyama, Jun 27 2023

Keywords

Links

Crossrefs

Cf. A001842, A050452, A363903.
Cf. A113415, A363902.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (d%4==3)*(d+1))/4;

Formula

a(n) = (1/4) * Sum_{d|n, d==3 mod 4} (d+1) = (A001842(n) + A050452(n))/4.
G.f.: Sum_{k>0} k * x^(4*k-1) / (1 - x^(4*k-1)).

A363971 Expansion of Sum_{k>0} k^2 * x^(3*k-1) / (1 - x^(3*k-1)).

Original entry on oeis.org

0, 1, 0, 1, 4, 1, 0, 10, 0, 5, 16, 1, 0, 26, 4, 10, 36, 1, 0, 54, 0, 17, 64, 10, 4, 82, 0, 26, 100, 5, 0, 131, 16, 37, 148, 1, 0, 170, 0, 63, 196, 26, 0, 242, 4, 65, 256, 10, 0, 294, 36, 82, 324, 1, 20, 396, 0, 101, 400, 54, 0, 442, 0, 131, 488, 17, 0, 566, 64, 174, 576, 10, 0, 626, 4, 170
Offset: 1

Views

Author

Seiichi Manyama, Jun 30 2023

Keywords

Crossrefs

Cf. A001822, A363902.
Cf. A103638, A363976.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, ((#+1)/3)^2 &, Mod[#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (d%3==2)*((d+1)/3)^2);

Formula

a(n) = Sum_{d|n, d==2 mod 3} ((d+1)/3)^2.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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