A029054 Expansion of 1/((1-x)*(1-x^3)*(1-x^8)*(1-x^9)).

1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 6, 7, 9, 9, 10, 12, 13, 15, 18, 19, 21, 24, 25, 27, 31, 33, 36, 41, 43, 46, 51, 53, 57, 63, 66, 71, 78, 81, 86, 93, 97, 103, 111, 116, 123, 132, 137, 144, 154, 160, 168, 179, 186, 195, 207

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 8 and 9. - Ilya Gutkovskiy, May 16 2017

Links

G. C. Greubel, 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, 1, 0, -1, -1, 0, 1, 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)=4, a(9)=6, a(10)=6, a(11)=7, a(12)=9, a(13)=9, a(14)=10, a(15)=12, a(16)=13, a(17)=15, a(18)=18, a(19)=19, a(20)=21, a(n)=a(n-1)+ a(n-3)- a(n-4)+ a(n-8)-a(n-10)-a(n-11)+a(n-13)-a(n-17)+a(n-18)+a(n-20)-a(n-21). - Harvey P. Dale, May 09 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^8)(1-x^9)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 0, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 6, 7, 9, 9, 10, 12, 13, 15, 18, 19, 21}, 60] (* Harvey P. Dale, May 09 2013 *)

Prog

(PARI) x='x+O('x^50); Vec(1/((1-x)*(1-x^3)*(1-x^8)*(1-x^9))) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A341451 A123576 A094824 * A341452 A008997 A341453

Adjacent sequences: A029051 A029052 A029053 * A029055 A029056 A029057

Keyword

nonn

Author

N. J. A. Sloane

Status

approved