A029162 Expansion of 1/((1-x^2)(1-x^3)(1-x^8)(1-x^10)).

1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 8, 6, 10, 8, 12, 10, 14, 12, 17, 14, 20, 17, 23, 20, 27, 23, 31, 27, 35, 31, 40, 35, 45, 40, 51, 45, 57, 51, 63, 57, 70, 63, 78, 70, 86, 78, 94, 86, 103, 94, 113, 103, 123, 113, 134, 123, 145, 134, 157, 145, 170, 157

Offset

0,7

Comments

Number of partitions of n into parts 2, 3, 8, and 10. - Stefano Spezia, Mar 07 2023

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

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

Formula

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)=3, a(9)=2, a(10)=4, a(11)=3, a(12)=5, a(13)=4, a(14)=6, a(15)=5, a(16)=8, a(17)=6, a(18)=10, a(19)=8, a(20)=12, a(21)=10, a(22)=14, a(n)=a(n-2)+ a(n-3)-a(n-5)+a(n-8)-a(n-11)-a(n-12)+a(n-15)-a(n-18)+a(n-20)+a(n-21)- a(n-23). - Harvey P. Dale, Nov 06 2012

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^8)(1-x^10)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 0, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 8, 6, 10, 8, 12, 10, 14}, 60] (* Harvey P. Dale, Nov 06 2012 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^8)*(1-x^10)) + O(x^70)) \\ Michel Marcus, Mar 08 2023

Crossrefs

Sequence in context: A028242 A030451 A241825 * A325132 A225854 A371973

Adjacent sequences: A029159 A029160 A029161 * A029163 A029164 A029165

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved