A025894 Expansion of 1/((1-x^5)*(1-x^10)*(1-x^11)).

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 3, 2, 1, 0, 0, 3, 2, 1, 0, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 7, 5, 4, 3, 2, 8, 6, 5, 4, 3, 9, 7, 5, 4, 3, 10, 8, 6, 5, 4, 11, 9, 7, 5, 4

Offset

0,11

Comments

a(n) is the number of partitions of n into parts 5, 10, and 11. - 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 (0,0,0,0,1,0,0,0,0,1,1,0,0,0,-1,-1,0,0,0,0,-1,0,0,0,0,1).

Formula

a(n) = floor((n*(89*n+54) + 10*(n+8)*floor(n/5))/100) - floor((10*n^2 + 7*n - 6)/11). - Hoang Xuan Thanh, Sep 22 2025

Mathematica

CoefficientList[Series[1/((1-x^5)(1-x^10)(1-x^11)), {x, 0, 120}], x] (* Harvey P. Dale, Aug 07 2019 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 120); Coefficients(R!( 1/((1-x^5)*(1-x^10)*(1-x^11)) )); // G. C. Greubel, Jan 17 2024
(SageMath)
def A025894_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^5)*(1-x^10)*(1-x^11)) ).list()
A025894_list(120) # G. C. Greubel, Jan 17 2024
(PARI) a(n) = ((n+10)*(n+60)/1100 - (n+8)*(n%5)/50 + ((10*n^2+7*n+5)%11)/11)\1 \\ Hoang Xuan Thanh, Sep 22 2025

Crossrefs

Cf. A025893, A025895, A025896.

Sequence in context: A352245 A227834 A397697 * A339087 A051127 A070176

Adjacent sequences: A025891 A025892 A025893 * A025895 A025896 A025897

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved