A029158 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^10)).

1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 3, 5, 5, 6, 6, 8, 8, 9, 10, 12, 12, 14, 15, 17, 17, 20, 21, 23, 24, 28, 28, 31, 33, 36, 37, 41, 43, 46, 48, 53, 54, 59, 61, 66, 68, 73, 76, 81, 84, 90, 93, 99, 102, 109, 112, 119, 123, 130, 134, 142, 146, 154, 159, 167, 172, 181

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 7, and 10. - Hoang Xuan Thanh, Oct 05 2025

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^3+33*n^2+354*n+1800)/2520 - n*(n mod 2)/40 - (n mod 3)/9 + ((2*n^3+3*n^2+n+2) mod 7)/7). - Hoang Xuan Thanh, Oct 05 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^7)(1-x^10)), {x, 0, 60}], x] (* Harvey P. Dale, Sep 06 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^7)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 18 2020

Crossrefs

Sequence in context: A387223 A054860 A098745 * A241953 A156197 A155162

Adjacent sequences: A029155 A029156 A029157 * A029159 A029160 A029161

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jinyuan Wang, Mar 18 2020

Status

approved