A025799 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^10)).

1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 4, 4, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 13, 11, 14, 13, 15, 14, 17, 15, 18, 17, 20, 18, 22, 20, 23, 22, 25, 23, 27, 25, 29, 27, 31, 29, 33, 31, 35, 33, 37, 35, 40, 37, 42, 40, 44, 42, 47, 44, 49, 47, 52, 49, 55, 52, 57, 55, 60, 57

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Comments

Number of partitions of n into parts 2, 3, and 10. - Hoang Xuan Thanh, Aug 21 2025

Examples

			G.f. = 1 + x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + 2*x^8 + 2*x^9 + 3*x^10 + 2*x^11 + ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,0,0,0,0,1,0,-1,-1,0,1).

Crossrefs

Cf. A008672, A028242.

Programs

Mathematica

A025799[n_] := Floor[(n^2 + 15*n + 3*(-1)^n*(n + 7) + 99)/120];
Array[A025799, 100, 0] (* Paolo Xausa, Aug 25 2025 *)

PARI

{a(n) = if( n<-14, a(-15 - n), polcoeff( 1 / ((1 - x^2) * (1 - x^3) * (1 - x^10)) + x * O(x^n), n))}; /* Michael Somos, Mar 2003 */

PARI

{a(n) = n = (n - 3*(n%2)) / 2; (n^2 + 9*n)\30 + 1}; /* Michael Somos, Nov 16 2005 */

Formula

G.f.: 1/((1-x^2)(1-x^3)(1-x^10)).

a(n) = A008672( A028242(n - 2)). a(2*n + 3) = a(2*n) = A008672(n).- Michael Somos, Mar 2003

a(n) = a(-15 - n) for all n in Z. - Michael Somos, Nov 16 2005

a(n) = floor((n^2 + 15*n + 3*(n+7)*(-1)^n + 99)/120). - Hoang Xuan Thanh, Aug 21 2025