A025900 - OEIS

A025900

Expansion of 1/((1-x^6)*(1-x^7)*(1-x^11)).

1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,19

COMMENTS

a(n) is the number of partitions of n into parts 6, 7, and 11. - Michel Marcus, Jan 23 2024

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1,0,0,0,1,0,-1,0,0,0,-1,-1,0,0,0,0,0,1).

FORMULA

a(n) = floor((5*n^2+12*n+12)/12) - floor((n^2+3*n+4)/7) - floor((3*n^2+6*n+5)/11). - Hoang Xuan Thanh, Sep 24 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^11)), {x, 0, 120}], x] (* Harvey P. Dale, Apr 30 2011 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^(11))) )); // G. C. Greubel, Jan 23 2024

(SageMath)

def A025900_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( 1/((1-x^6)*(1-x^7)*(1-x^(11)))).list()

A025900_list(100) # G. C. Greubel, Jan 23 2024

(PARI) a(n) = (n^2+24*n-24)/924 + ((n^2+3*n+4)%7)/7 + ((3*n^2+6*n+5)%11)/11 - ((5*n^2)%12)/12 \\ Hoang Xuan Thanh, Sep 24 2025

CROSSREFS

Cf. A025896, A025897, A025898, A025899, A025901, A025902, A025903.

Sequence in context: A329037 A279794 A395082 * A118383 A115766 A108339

Adjacent sequences: A025897 A025898 A025899 * A025901 A025902 A025903

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved