A029034 Expansion of 1/((1-x)(1-x^3)(1-x^4)(1-x^8)).

1, 1, 1, 2, 3, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 20, 24, 26, 29, 33, 38, 41, 45, 50, 57, 61, 66, 73, 81, 86, 93, 101, 111, 118, 126, 136, 148, 156, 166, 178, 192, 202, 214, 228, 244, 256, 270, 286, 305, 319, 335, 354

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 4 and 8. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..51.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 0, -1, 0, -1, 2, -1, 0, -1, 0, 1, 0, 1, -1).

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=3, a(6)=4, a(7)=5, a(8)=7, a(9)=8, a(10)=9, a(11)=11, a(12)=14, a(13)=15, a(14)=17, a(15)=20, a(n)=a(n-1)+a(n-3)-a(n-5)-a(n-7)+2*a(n-8)-a(n-9)-a(n-11)+ a(n-13)+ a(n-15)-a(n-16). - Harvey P. Dale, Jul 21 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^8)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 1, 0, -1, 0, -1, 2, -1, 0, -1, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 3, 4, 5, 7, 8, 9, 11, 14, 15, 17, 20}, 60] (* Harvey P. Dale, Jul 21 2013 *)

Crossrefs

Sequence in context: A125616 A367220 A141472 * A343941 A280127 A237977

Adjacent sequences: A029031 A029032 A029033 * A029035 A029036 A029037

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved