A025832 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^10)).

1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 7, 6, 7, 7, 8, 7, 9, 8, 9, 9, 11, 9, 11, 11, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 21, 19, 21, 21, 23, 21, 24, 23

Offset

0,11

Comments

Number of partitions of n into parts 3, 4, and 10. - Joerg Arndt, Aug 28 2013

Links

Table of n, a(n) for n=0..67.

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

Formula

a(n) = a(n-3) + a(n-4) - a(n-7) + a(n-10) - a(n-13) - a(n-14) + a(n-17). - R. J. Mathar, Jun 04 2013

a(n) = floor((n^2 + 17*n + 216)/240 + (n+8)*(-1)^n/80 + (n mod 3)*(1 -(n mod 3))/10). - Hoang Xuan Thanh, Aug 26 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^4)(1-x^10)), {x, 0, 70}], x] (* Harvey P. Dale, May 03 2021 *)

Prog

(PARI) a(n)=floor((n%3<2)/3+(-1)^(n\5)/10+(2*n^2+34*n+221)/480+(2*n+17)*(-1)^n/160); \\ Tani Akinari, Aug 28 2013
(PARI) a(n) = (n^2+17*n+216 +3*n*(-1)^n + 24*((-1)^n + n%3*(1-n%3)))\240 \\ Hoang Xuan Thanh, Aug 26 2025

Crossrefs

Sequence in context: A053280 A289122 A370809 * A320385 A112222 A112220

Adjacent sequences: A025829 A025830 A025831 * A025833 A025834 A025835

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved