A029203 - OEIS

A029203

Expansion of 1/((1-x^2)*(1-x^5)*(1-x^7)*(1-x^12)).

1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 4, 2, 5, 3, 5, 5, 5, 7, 6, 8, 8, 8, 11, 9, 13, 11, 14, 14, 15, 17, 17, 19, 20, 21, 24, 23, 27, 26, 30, 30, 33, 34, 36, 38, 40, 42, 45, 46, 50, 50, 55, 55, 60, 61, 65, 67, 70, 73, 77, 79, 84

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OFFSET

0,8

COMMENTS

Number of partitions of n into parts 2, 5, 7, and 12. - 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 (0,1,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,1,0,-1).

FORMULA

a(n) = floor((n^3+39*n^2+504*n+2700)/5040 - (n+16)*(n mod 2)/48 + ((3*n^3+2*n^2+2*n) mod 5)/5 + ((n^3+4*n^2+5) mod 7)/7 + ((n mod 6)-((7*n) mod 12))/12). - Hoang Xuan Thanh, Oct 15 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^7) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^5)*(1-x^7)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

CROSSREFS

Sequence in context: A353339 A291708 A163822 * A363526 A159805 A208216

Adjacent sequences: A029200 A029201 A029202 * A029204 A029205 A029206

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved