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.

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A175630 a(n) = n-th pentagonal number mod (n+2).

Original entry on oeis.org

0, 1, 1, 2, 4, 0, 3, 7, 2, 7, 1, 7, 0, 7, 15, 7, 16, 7, 17, 7, 18, 7, 19, 7, 20, 7, 21, 7, 22, 7, 23, 7, 24, 7, 25, 7, 26, 7, 27, 7, 28, 7, 29, 7, 30, 7, 31, 7, 32, 7, 33, 7, 34, 7, 35, 7, 36, 7, 37, 7, 38, 7, 39, 7, 40, 7, 41, 7, 42, 7, 43, 7, 44, 7, 45, 7, 46, 7, 47, 7, 48, 7, 49, 7, 50, 7, 51
Offset: 0

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Author

Zak Seidov, Jul 29 2010

Keywords

Comments

k>=0, a(7+2*k)=7, (for odd indices >=7),
also k>=0, a(14+2*k)=15+k, (for even indices >=14).

Crossrefs

Cf. A000326 Pentagonal numbers:n(3n-1)/2, A179820 a(n) = n-th triangular number mod (n+2).

Programs

  • Mathematica
    Table[Mod[n(3n-1)/2,n+2],{n,0,200}]
    With[{nn=90},Mod[PolygonalNumber[5,Range[0,nn]],Range[2,nn+2]]] (* Requires Mathematica version 10 or later *)  (* Harvey P. Dale, Jun 28 2020 *)

Formula

From Chai Wah Wu, Oct 12 2018: (Start)
a(n) = 2*a(n-2) - a(n-4) for n > 16.
G.f.: x*(-14*x^15 + 16*x^13 - 7*x^8 + 9*x^6 - 4*x^5 - 3*x^4 + 2*x^3 + x + 1)/((x - 1)^2*(x + 1)^2). (End)
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