A025835 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^6)).

1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 1, 2, 3, 1, 2, 4, 2, 3, 5, 2, 4, 6, 3, 5, 7, 4, 6, 8, 5, 7, 10, 6, 8, 11, 7, 10, 13, 8, 11, 14, 10, 13, 16, 11, 14, 18, 13, 16, 20, 14, 18, 22, 16, 20, 24, 18, 22, 26, 20, 24, 29, 22, 26, 31, 24, 29

Offset

0,7

Comments

Number of partitions of n into parts 3, 5, and 6. - Hoang Xuan Thanh, Sep 01 2025

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = a(n-3)+a(n-5)+a(n-6)-a(n-8)-a(n-9)-a(n-11)+a(n-14) with a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=2, a(7)=0, a(8)=1, a(9)=2, a(10)=1, a(11)=2, a(12)=3, a(13)=1. - Harvey P. Dale, Jun 09 2015

a(n) = floor((n^2 + 4*n + 40 + 10*(n+7)*((n+2) mod 3))/180). - Hoang Xuan Thanh, Sep 01 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^6)), {x, 0, 90}], x] (* or *) LinearRecurrence[ {0, 0, 1, 0, 1, 1, 0, -1, -1, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 1, 2, 3, 1}, 90] (* Harvey P. Dale, Jun 09 2015 *)

Prog

(PARI) a(n) = (n^2 + 4*n + 100 + 10*(n+4)*((n+2)%3))\180 \\ Hoang Xuan Thanh, Sep 01 2025

Crossrefs

Sequence in context: A237203 A339444 A029389 * A029277 A077905 A131331

Adjacent sequences: A025832 A025833 A025834 * A025836 A025837 A025838

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved