A025896 Expansion of 1/((1-x^5)*(1-x^11)*(1-x^12)).

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

Offset

0,23

Comments

a(n) is the number of partitions of n into parts 5, 11, and 12. - Joerg Arndt, Jan 17 2024

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((n+2)*(15*n+38)/44) - floor((n+1)*(n+2)/5) - 2*floor((n+3)^2/11) + floor((n+2)^2/24) + floor((n+14)/22) - floor((n+13)/22). - Hoang Xuan Thanh, Sep 23 2025

Mathematica

CoefficientList[Series[1/((1-x^5)*(1-x^11)*(1-x^12)), {x, 0, 120}], x] (* G. C. Greubel, Jan 17 2024 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 120); Coefficients(R!( 1/((1-x^5)*(1-x^11)*(1-x^12)) )); // G. C. Greubel, Jan 17 2024
(SageMath)
def A025896_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^11)*(1-x^12)) ).list()
A025896_list(120) # G. C. Greubel, Jan 17 2024
(PARI) a(n) = ((n+2)*(15*n+38))\44 - ((n+1)*(n+2))\5 - 2*((n+3)^2\11) + (n+2)^2\24 + (n%22==8) \\ Hoang Xuan Thanh, Sep 23 2025

Crossrefs

Cf. A025893, A025894, A025895, A025897.

Sequence in context: A043278 A125238 A380698 * A050432 A343747 A381900

Adjacent sequences: A025893 A025894 A025895 * A025897 A025898 A025899

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved