A029060 Expansion of 1/((1-x)*(1-x^3)*(1-x^10)*(1-x^11)).

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 37, 40, 43, 47, 50, 53, 57, 60, 63, 67, 71, 75, 80, 85, 90, 95, 100, 105, 110, 115, 121, 127, 133, 140, 147, 154

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 10 and 11. - Ilya Gutkovskiy, May 16 2017

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=3, a(8)=3, a(9)=4, a(10)=5, a(11)=6, a(12)=7, a(13)=8, a(14)=9, a(15)=10, a(16)=11, a(17)=12, a(18)=13, a(19)=14, a(20)=16, a(21)=18, a(22)=20, a(23)=22, a(24)=24, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-10)-a(n-12)-a(n-13)+a(n-15)- a(n-21)+ a(n-22)+a(n-24)-a(n-25). - Harvey P. Dale, Jan 11 2014

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^10)(1-x^11)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 20, 22, 24}, 60] (* Harvey P. Dale, Jan 11 2014 *)

Prog

(PARI) a(n)=floor((2*n^3+75*n^2+822*n+4312)/3960+[-1, -1, -1, 1, 1, 1, 2, 1, -1, -2][n%10+1]/5+((2*n+2)%3-1)/9) \\ Tani Akinari, May 22 2014
(PARI) x='x+O('x^50); Vec(1/((1-x)*(1-x^3)*(1-x^10)*(1-x^11))) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A337206 A334576 A081607 * A184258 A219291 A029160

Adjacent sequences: A029057 A029058 A029059 * A029061 A029062 A029063

Keyword

nonn

Author

N. J. A. Sloane

Status

approved