A029046 Expansion of 1/((1-x)(1-x^3)(1-x^6)(1-x^8)).

1, 1, 1, 2, 2, 2, 4, 4, 5, 7, 7, 8, 11, 11, 13, 16, 17, 19, 23, 24, 27, 31, 33, 36, 42, 44, 48, 54, 57, 61, 69, 72, 78, 86, 90, 96, 106, 110, 118, 128, 134, 142, 154, 160, 170, 182, 190, 200, 215, 223, 235, 250, 260

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 6 and 8. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..52.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 0, 1, -1, 1, -2, 1, -1, 1, 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)=4, a(7)=4, a(8)=5, a(9)=7, a(10)=7, a(11)=8, a(12)=11, a(13)=11, a(14)=13, a(15)=16, a(16)=17, a(17)=19, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-6)-a(n-7)+a(n-8)- 2*a(n-9)+ a(n-10)-a(n-11)+a(n-12)-a(n-14)+a(n-15)+a(n-17)-a(n-18). - Harvey P. Dale, Apr 05 2014

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^8)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 0, 1, -1, 1, -2, 1, -1, 1, 0, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 2, 4, 4, 5, 7, 7, 8, 11, 11, 13, 16, 17, 19}, 80] (* Harvey P. Dale, Apr 05 2014 *)

Crossrefs

Sequence in context: A035682 A054543 A240861 * A035372 A035576 A272397

Adjacent sequences: A029043 A029044 A029045 * A029047 A029048 A029049

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved