A029009 Expansion of 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^9)).

1, 1, 2, 2, 4, 4, 6, 6, 9, 10, 13, 14, 18, 20, 24, 26, 31, 34, 40, 43, 50, 54, 62, 66, 75, 80, 90, 96, 107, 114, 126, 134, 147, 156, 170, 180, 196, 207, 224, 236, 255, 268, 288, 302, 324, 340, 363, 380, 405, 424, 450

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 4 and 9. - Ilya Gutkovskiy, May 13 2017

Links

Table of n, a(n) for n=0..50.

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=4, a(5)=4, a(6)=6, a(7)=6, a(8)=9, a(9)=10, a(10)=13, a(11)=14, a(12)=18, a(13)=20, a(14)=24, a(15)=26, a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7)+a(n-9)-a(n-10)- a(n-11)+ a(n-12)-a(n-13)+a(n-14)+a(n-15)-a (n-16). [Harvey P. Dale, May 05 2012]

a(n) = floor((n^3 + 24*n^2 + 153*n + 432)/432 + n/16 * [(n mod 2)=0]) + [(n mod 18)=4]. - Hoang Xuan Thanh, Jul 01 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^4)(1-x^9)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1, 1, -1, -1, 1, 0, 1, -1, -1, 1, -1, 1, 1, -1}, {1, 1, 2, 2, 4, 4, 6, 6, 9, 10, 13, 14, 18, 20, 24, 26}, 60] (* Harvey P. Dale, May 05 2012 *)

Crossrefs

Sequence in context: A358206 A001310 A328422 * A340280 A340279 A343100

Adjacent sequences: A029006 A029007 A029008 * A029010 A029011 A029012

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved