A029004 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^10)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 15, 17, 21, 24, 28, 32, 37, 41, 47, 52, 59, 65, 73, 80, 89, 97, 107, 116, 127, 137, 150, 161, 175, 188, 203, 217, 234, 249, 267, 284, 304, 322, 344, 364, 387, 409, 434, 457, 484, 509

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 3, and 10. [Joerg Arndt, Jul 07 2013]

Links

Table of n, a(n) for n=0..49.

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=10, a(9)=12, a(10)=15, a(11)=17, a(12)=21, a(13)=24, a(14)=28, a(15)=32, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6)+a(n-10)-a(n-11)- a(n-12)+ a(n-14)+a(n-15)-a(n-16). - Harvey P. Dale, Jun 01 2013

a(n) = floor((2*n^3+48*n^2+327*n+927+9*(n+1)*(-1)^n)/720). - Tani Akinari, Jul 07 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^10)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, 0, -1, -1, 1, 0, 0, 0, 1, -1, -1, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 15, 17, 21, 24, 28, 32}, 60] (* Harvey P. Dale, Jun 01 2013 *)

Crossrefs

Sequence in context: A132154 A049807 A008753 * A332728 A008752 A029003

Adjacent sequences: A029001 A029002 A029003 * A029005 A029006 A029007

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved