A029216 Expansion of 1/((1-x^2)*(1-x^6)*(1-x^7)*(1-x^10)).

1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 3, 1, 4, 2, 5, 2, 6, 3, 7, 4, 9, 5, 10, 6, 12, 7, 14, 9, 16, 10, 19, 12, 21, 14, 24, 16, 27, 19, 30, 21, 34, 24, 38, 27, 42, 30, 46, 34, 51, 38, 56, 42, 61, 46, 67, 51, 73, 56, 79, 61, 86, 67, 93

Offset

0,7

Comments

Number of partitions of n into parts 2, 6, 7, and 10. - Joerg Arndt, Jun 02 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((n^3+48*n^2+684*n+3600)/5040 - (n^2+25*n+42)*(n mod 2)/240 + ((n^3+6*n^2+5*n+2) mod 7)/7). - Hoang Xuan Thanh, Oct 21 2025

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^6) (1 - x^7) (1 - x^10)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^6)*(1-x^7)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A224708 A322023 A029229 * A153174 A138222 A138224

Adjacent sequences: A029213 A029214 A029215 * A029217 A029218 A029219

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved