A029014 Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^9)).

1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 20, 23, 26, 29, 33, 37, 42, 46, 51, 56, 62, 68, 74, 81, 88, 96, 104, 112, 121, 130, 140, 150, 161, 172, 184, 196, 209, 222, 236, 250, 265, 281, 297, 314, 331, 349, 368, 387

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5 and 9. - Ilya Gutkovskiy, May 13 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=3, a(5)=4, a(6)=5, a(7)=6, a(8)=7, a(9)=9, a(10)=11, a(11)=13, a(12)=15, a(13)=17, a(14)=20, a(15)=23, a(16)=26, a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-5)-a(n-6)-a(n-7)+a(n-8)+ a(n-9)-a(n-10)-a(n-11)+a(n-12)-a(n-14)+a(n-15)+a(n-16)-a(n-17) [From Harvey P. Dale, Mar 03 2012]

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^5)(1-x^9)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 1, -1, -1, 1, 1, -1, -1, 1, 0, -1, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 20, 23, 26}, 60] (* Harvey P. Dale, Mar 03 2012 *)

Crossrefs

Sequence in context: A017863 A242634 A088567 * A304631 A298603 A134345

Adjacent sequences: A029011 A029012 A029013 * A029015 A029016 A029017

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved