A029281 - OEIS

A029281

Expansion of 1/((1-x^3)*(1-x^5)*(1-x^7)*(1-x^12)).

1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 4, 2, 4, 4, 4, 5, 5, 6, 5, 8, 7, 7, 10, 8, 10, 11, 11, 12, 13, 14, 14, 17, 16, 17, 20, 19, 21, 23, 23, 24, 27, 27, 28, 32, 31, 33, 36, 36, 38, 41, 42, 43, 47, 47, 49, 54, 53, 56, 60, 60, 63, 67, 68, 70, 75, 76, 78, 84

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OFFSET

0,11

COMMENTS

Number of partitions of n into parts 3, 5, 7, and 12. - Vincenzo Librandi, Jun 04 2014

LINKS

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

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

FORMULA

a(n) = floor((n+12)*((2*n^2+57*n+156)/420 + ((2*n^2+1) mod 3))/36 + ((2*n^3+n^2+2) mod 5)/5 + ((3*n^3+6*n^2+1) mod 7)/7). - Hoang Xuan Thanh, Mar 30 2026

MATHEMATICA

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^7) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 04 2014 *)

PROG

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^7)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

CROSSREFS

Sequence in context: A298742 A086415 A069013 * A126792 A097367 A130211

Adjacent sequences: A029278 A029279 A029280 * A029282 A029283 A029284

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved