A025897 Expansion of 1/((1-x^6)*(1-x^7)*(1-x^8)).

1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 5, 4, 5, 4, 5, 4, 6, 5, 6, 5, 6, 5, 7, 6, 8, 6, 7, 6, 8, 7, 9, 8, 9, 7, 9, 8, 10, 9, 11, 9, 11, 9, 11, 10, 12, 11

Offset

0,15

Comments

a(n) is the number of partitions of n into parts 6, 7, and 8. - Joerg Arndt, Jan 22 2024

Links

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

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

Formula

a(n) = a(n-6) + a(n-7) + a(n-8) - a(n-13) - a(n-14) - a(n-15) + a(n-21). - Harvey P. Dale, Aug 17 2014

a(n) = floor((n^2+21*n+686)/672 + (n+10)*(-1)^n/96 - ((3*n^2) mod 7)/7). - Hoang Xuan Thanh, Sep 24 2025

Mathematica

CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^8)), {x, 0, 100}], x] (* Harvey P. Dale, Aug 17 2014 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^8)) )); // G. C. Greubel, Jan 22 2024
(SageMath)
def A025897_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^6)*(1-x^7)*(1-x^8))).list()
A025897_list(100) # G. C. Greubel, Jan 22 2024
(PARI) a(n) = (n^2+21*n+686 + 7*(n+10)*(-1)^n - 96*((3*n^2)%7))\672 \\ Hoang Xuan Thanh, Sep 24 2025

Crossrefs

Cf. A025896, A025898, A025899, A025900, A025901, A025902, A025903.

Sequence in context: A020944 A287729 A367582 * A029421 A156749 A340390

Adjacent sequences: A025894 A025895 A025896 * A025898 A025899 A025900

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved