A025781 Expansion of 1/((1-x)(1-x^5)(1-x^12)).

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 5, and 12. - Joerg Arndt, Mar 18 2013

Up to and including a(21) this is the same as the expansion of Product_{k>=1} 1/(1-x^(k*(3*k-1)/2)), which appears as a convolution factor in A095699. - R. J. Mathar, Mar 18 2013

Links

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

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-x^5)(1-x^12)),{x,0,70}],x] (* or *) LinearRecurrence[{1,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,-1,1},{1,1,1,1,1,2,2,2,2,2,3,3,4,4,4,5,5,6},70] (* Harvey P. Dale, May 11 2014 *)

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=2, a(6)=2, a(7)=2, a(8)=2, a(9)=2, a(10)=3, a(11)=3, a(12)=4, a(13)=4, a(14)=4, a(15)=5, a(16)=5, a(17)=6, a(n)=a(n-1)+a(n-5)-a(n-6)+a(n-12)-a(n-13)-a(n-17)+a(n-18). - Harvey P. Dale, May 11 2014