0,7

Number of partitions of n into parts 2, 3, 9, and 12. - Hoang Xuan Thanh, Oct 07 2025

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

a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=1, a(8)=2, a(9)=3, a(10)=2, a(11)=3, a(12)=5, a(13)=3, a(14)=5, a(15)=6, a(16)=5, a(17)=6, a(18)=9, a(19)=6, a(20)=9, a(21)=11, a(22)=9, a(23)=11, a(24)=15, a(25)=11, a(n)=a(n-2)+a(n-3)-a(n-5)+a(n-9)-a(n-11)- a(n-15)+ a(n-17)-a(n-21)+a(n-23)+a(n-24)-a(n-26). - Harvey P. Dale, Feb 07 2015

a(n) = floor((n^3+33*n^2+336*n+3300)/3888 + (n^2+26*n+49)*((n+2) mod 3)/648 - n*(n mod 2)/48 - n*((2*n^2+n) mod 3)/324). - Hoang Xuan Thanh, Oct 07 2025

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^9)(1-x^12)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 5, 3, 5, 6, 5, 6, 9, 6, 9, 11, 9, 11, 15, 11}, 100] (* Harvey P. Dale, Feb 07 2015 *)

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^9)*(1-x^12)) + O(x^60)) \\ Hoang Xuan Thanh, Oct 07 2025

Sequence in context: A165477 A318687 A119994 * A161103 A337879 A147301

Adjacent sequences: A029164 A029165 A029166 * A029168 A029169 A029170

nonn,easy

approved