A029229 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^8)*(1-x^12)).

1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 3, 1, 4, 2, 5, 2, 5, 3, 6, 4, 7, 5, 9, 5, 10, 6, 12, 7, 13, 9, 15, 10, 16, 12, 19, 13, 21, 15, 24, 16, 26, 19, 29, 21, 31, 24, 35, 26, 38, 29, 42, 31, 45, 35, 50, 38, 53, 42, 58, 45, 62, 50

Offset

0,9

Comments

Number of partitions of n into parts 2, 7, 8, and 12. - Vincenzo Librandi, Jun 02 2014

Links

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

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

Formula

a(n) = floor((n^3+54*n^2+828*n+4352)/8064 - (n^2+29*n+31)*(n mod 2)/384 + n*((n^2+n+2) mod 4)/192 + ((5*n^3+4*n^2+3*n+4) mod 7)/7). - Hoang Xuan Thanh, Oct 25 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^7)(1-x^8)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Mar 19 2011 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^7)*(1-x^8)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A105259 A224708 A322023 * A029216 A153174 A138222

Adjacent sequences: A029226 A029227 A029228 * A029230 A029231 A029232

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1999

Status

approved