A029006 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^12)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 20, 22, 26, 30, 34, 38, 44, 48, 54, 60, 66, 72, 81, 87, 96, 105, 114, 123, 135, 144, 156, 168, 180, 192, 208, 220, 236, 252, 268, 284, 304, 320, 340, 360, 380, 400, 425, 445

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 3 and 12. - Ilya Gutkovskiy, May 13 2017

Links

Table of n, a(n) for n=0..49.

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=10, a(9)=12, a(10)=14, a(11)=16, a(12)=20, a(13)=22, a(14)=26, a(15)=30, a(16)=34, a(17)=38, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6)+ a(n-12)- a(n-13)- a(n-14)+a(n-16)+a(n-17)-a(n-18). - Harvey P. Dale, Nov 01 2015

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^12)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 20, 22, 26, 30, 34, 38}, 50] (* Harvey P. Dale, Nov 01 2015 *)

Crossrefs

Sequence in context: A008757 A008756 A008755 * A085756 A350896 A008754

Adjacent sequences: A029003 A029004 A029005 * A029007 A029008 A029009

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved