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.

A109699 Number of partitions of n into parts each equal to 3 mod 5.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 4, 2, 4, 4, 3, 5, 4, 5, 6, 5, 7, 6, 8, 8, 7, 11, 9, 10, 13, 10, 14, 14, 14, 17, 16, 19, 19, 20, 24, 21, 27, 27, 27, 33, 30, 35, 38, 36, 44, 42, 47, 51, 50, 58, 57, 63, 68, 66, 79, 76, 82, 92, 88, 101, 104, 107, 120
Offset: 0

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Author

Erich Friedman, Aug 07 2005

Keywords

Examples

			a(21)=3 since 21 = 18+3 = 13+8 = 3+3+3+3+3+3+3
		

Crossrefs

Cf. A284281.

Programs

  • Maple
    g:=1/product(1-x^(3+5*j),j=0..25): gser:=series(g,x=0,85): seq(coeff(gser,x,n),n=0..80); # Emeric Deutsch, Mar 30 2006
  • Mathematica
    nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+3)),{k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)
    Join[{1},Table[Length[Select[IntegerPartitions[n],Union[Mod[#,5]]=={3}&]],{n,80}]] (* Harvey P. Dale, Dec 01 2024 *)
  • PARI
    Vec(prod(k=0, 100, 1/(1 - x^(5*k + 3))) + O(x^111)) \\ Indranil Ghosh, Mar 24 2017

Formula

G.f.: 1/product(1-x^(3+5j), j=0..infinity). - Emeric Deutsch, Mar 30 2006
a(n) ~ Gamma(3/5) * exp(Pi*sqrt(2*n/15)) / (2^(9/5) * 3^(3/10) * 5^(1/5) * Pi^(2/5) * n^(4/5)) * (1 + (11*Pi/(120*sqrt(30)) - 6*sqrt(6/5)/(5*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
a(n) = (1/n)*Sum_{k=1..n} A284281(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 24 2017

Extensions

More terms from Emeric Deutsch, Mar 30 2006