A025901 Expansion of 1/((1-x^6)*(1-x^7)*(1-x^12)).

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

Offset

0,13

Comments

a(n) is the number of partitions of n into parts 6, 7, and 12. - Michel Marcus, 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 (0,0,0,0,0,1,1,0,0,0,0,1,-1,0,0,0,0,-1,-1,0,0,0,0,0,1).

Formula

a(n) = floor((n+12)*(n+48 - 14*(n mod 6))/1008 + ((5*n^2+6*n+3) mod 7)/7). - Hoang Xuan Thanh, Sep 24 2025

Mathematica

CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^12)), {x, 0, 100}], x] (* Harvey P. Dale, Nov 27 2020 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^(12))) )); // G. C. Greubel, Jan 23 2024
(SageMath)
def A025901_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^6)*(1-x^7)*(1-x^(12)))).list()
A025901_list(100) # G. C. Greubel, Jan 23 2024
(PARI) a(n) = ((n+12)*(n+48-14*(n%6)) + 144*((5*n^2+6*n+3)%7))\1008 \\ Hoang Xuan Thanh, Sep 24 2025

Crossrefs

Cf. A025896, A025897, A025898, A025899, A025900, A025902, A025903.

Sequence in context: A263250 A209287 A388712 * A204431 A386244 A361509

Adjacent sequences: A025898 A025899 A025900 * A025902 A025903 A025904

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved