A029147 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^10)).

1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 6, 6, 7, 9, 9, 10, 12, 12, 16, 15, 18, 19, 21, 24, 25, 27, 30, 31, 37, 36, 41, 43, 46, 51, 53, 56, 61, 63, 71, 71, 78, 81, 86, 93, 96, 101, 108, 111, 122, 123, 132, 137, 144, 153, 158, 165, 174, 179, 193, 195, 207, 214, 223, 235, 242, 251, 263, 270, 287, 291, 306, 315, 327, 342, 351, 363, 378, 387, 408, 414, 432, 444, 459, 477, 489, 504

Offset

0,6

Comments

a(n) is the number of partitions of n into parts 2, 3, 5, and 10. - Joerg Arndt, Aug 27 2025

Links

Table of n, a(n) for n=0..87.

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

Formula

a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=2, a(6)=2, a(7)=2, a(8)=3, a(9)=3, a(10)=5, a(11)=4, a(12)=6, a(13)=6, a(14)=7, a(15)=9, a(16)=9, a(17)=10, a(18)=12, a(19)=12, a(n) = a(n-2)+a(n-3)-a(n-7)-a(n-8)+2*a(n-10)-a(n-12)-a(n-13)+a(n-17)+a(n-18)-a(n-20). - Harvey P. Dale, Jan 19 2012

a(n) = floor((n^3+30*n^2+252*n+1800)/1800 - (n+6)*(n mod 2)/40 + n*((2*n^2+3) mod 5)/50). - Hoang Xuan Thanh, Oct 01 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^10)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, 0, 0, -1, -1, 0, 2, 0, -1, -1, 0, 0, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 6, 6, 7, 9, 9, 10, 12, 12}, 60] (* Harvey P. Dale, Jan 19 2012 *)

Prog

(PARI) a(n) = (n^3+30*n^2+252*n+1800-45*(n+6)*(n%2)+36*n*((2*n^2+3)%5))\1800 \\ Hoang Xuan Thanh, Oct 01 2025

Crossrefs

Sequence in context: A055256 A369985 A295630 * A228571 A224908 A386288

Adjacent sequences: A029144 A029145 A029146 * A029148 A029149 A029150

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved