A029090 Expansion of 1/((1-x)*(1-x^5)*(1-x^6)*(1-x^12)).

1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 7, 7, 7, 8, 9, 11, 13, 13, 14, 15, 17, 19, 22, 23, 24, 26, 28, 31, 35, 36, 38, 40, 43, 47, 52, 54, 56, 59, 63, 68, 74, 76, 79, 83, 88, 94, 101, 104, 108, 113, 119, 126, 134, 138, 143, 149, 156, 164, 174, 179, 185, 192, 200, 210

Offset

0,6

Comments

Number of partitions of n into parts 1, 5, 6 and 12. - Ilya Gutkovskiy, May 20 2017

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,0,-1,0,0,0,-1,2,-1,0,0,0,-1,0,1,0,0,0,1,-1).

Formula

a(n) = floor((n^3 + 36*n^2 + 333*n + 1728)/2160 + (n/144)*((n mod 6)-3)^2 + (1/5)*((2*n^3+2*n^2+n+1) mod 5)). - Hoang Xuan Thanh, Mar 13 2026

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^5) (1 - x^6) (1 -x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, May 27 2017 *)
LinearRecurrence[{1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 2, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 7, 7, 7, 8, 9, 11, 13, 13, 14, 15, 17, 19}, 100] (* Harvey P. Dale, Apr 29 2018 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-x^5)*(1-x^6)*(1-x^12)))); // Vincenzo Librandi, May 27 2017
(PARI) a(n) = floor((n^3+36*n^2+333*n+2162)/2160 + (n/144)*((n%6)-3)^2 + (1/5)*((n%30==12)-(n%30==9))) \\ Hoang Xuan Thanh, Aug 09 2025

Crossrefs

Sequence in context: A120505 A029109 A257998 * A364882 A029089 A358468

Adjacent sequences: A029087 A029088 A029089 * A029091 A029092 A029093

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved