A025899 Expansion of 1/((1-x^6)*(1-x^7)*(1-x^10)).

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

Offset

0,21

Comments

a(n) is the number of partitions of n into parts 6, 7, and 10. - Joerg Arndt, 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 (0,0,0,0,0,1,1,0,0,1,0,0,-1,0,0,-1,-1,0,0,0,0,0,1).

Formula

a(n) = floor((n^2+23*n+403)/840 + (n+12)*(-1)^n/120 + ((6*n^2+5*n+3) mod 7)/7). - Hoang Xuan Thanh, Sep 24 2025

Mathematica

CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^10)), {x, 0, 100}], x](* Harvey P. Dale, Jul 20 2021 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^(10))) )); // G. C. Greubel, Jan 23 2024
(SageMath)
def A025899_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^6)*(1-x^7)*(1-x^(10)))).list()
A025899_list(100) # G. C. Greubel, Jan 23 2024
(PARI) a(n) = (n^2+23*n+403 + 7*(n+12)*(-1)^n + 120*((6*n^2+5*n+3)%7))\840 \\ Hoang Xuan Thanh, Sep 24 2025

Crossrefs

Cf. A025896, A025897, A025898, A025900, A025901, A025902, A025903.

Sequence in context: A184304 A363298 A025909 * A025869 A093320 A082370

Adjacent sequences: A025896 A025897 A025898 * A025900 A025901 A025902

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved