A029207 - OEIS

A029207

Expansion of 1/((1-x^2)*(1-x^5)*(1-x^8)*(1-x^12)).

1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 1, 4, 2, 4, 3, 5, 4, 6, 4, 8, 5, 9, 6, 11, 8, 12, 9, 14, 11, 16, 12, 19, 14, 21, 16, 24, 19, 26, 21, 30, 24, 33, 26, 37, 30, 40, 33, 45, 37, 49, 40, 54, 45, 58, 49, 64, 54, 69, 58, 76, 64, 81, 69

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OFFSET

0,9

COMMENTS

Number of partitions of n into parts 2, 5, 8, and 12. - Hoang Xuan Thanh, Oct 15 2025

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,-1,1,0,-1,0,1,-1,-1,1,0,-1,0,1,-1,0,1,0,0,1,0,-1).

FORMULA

a(n) = floor((n^3+48*n^2+660*n+2736)/5760 - (n^2+27*n)*(n mod 2)/384 + (n+12)*((n^3+n^2+2*n+2) mod 4)/192 - floor(n/12)*((n^3+3*n) mod 4)/16 + ((2*n^3+n^2+2) mod 5)/5). - Hoang Xuan Thanh, Oct 15 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^8) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

LinearRecurrence[{0, 1, 0, 0, 1, 0, -1, 1, 0, -1, 0, 1, -1, -1, 1, 0, -1, 0, 1, -1, 0, 1, 0, 0, 1, 0, -1}, {1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 1, 4, 2, 4, 3, 5, 4, 6, 4, 8, 5, 9, 6, 11, 8, 12}, 100] (* Harvey P. Dale, May 15 2021 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^5)*(1-x^8)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

CROSSREFS

Sequence in context: A194943 A087145 A117172 * A111902 A316211 A329480

Adjacent sequences: A029204 A029205 A029206 * A029208 A029209 A029210

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved