A025903 Expansion of 1/((1-x^6)*(1-x^8)*(1-x^11)).

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

Offset

0,23

Comments

a(n) is the number of partitions of n into parts 6, 8, and 11. - Michel Marcus, Jan 24 2024

Links

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

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

Formula

a(n) = floor((n^2+25*n+236)/1056 + (n+8)*(-1)^n/96 + ((4*n^2+n+9) mod 11)/11). - Hoang Xuan Thanh, Sep 25 2025

Mathematica

CoefficientList[Series[1/((1-x^6)(1-x^8)(1-x^11)), {x, 0, 80}], x] (* Harvey P. Dale, May 22 2018 *)

Prog

(PARI) Vec(1/((1-x^6)*(1-x^8)*(1-x^11)) + O(x^90)) \\ Jinyuan Wang, Feb 28 2020
(PARI) a(n) = (n^2+25*n+236 + 11*(n+8)*(-1)^n + 96*((4*n^2+n+9)%11))\1056 \\ Hoang Xuan Thanh, Sep 25 2025
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^8)*(1-x^11)) )); // G. C. Greubel, Jan 23 2024
(SageMath)
def A025903_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^6)*(1-x^8)*(1-x^11)) ).list()
A025903_list(100) # G. C. Greubel, Jan 23 2024

Crossrefs

Cf. A025902, A025904.

Sequence in context: A084217 A381587 A245548 * A175327 A101211 A380450

Adjacent sequences: A025900 A025901 A025902 * A025904 A025905 A025906

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved