A029305 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^11)*(1-x^12)).

1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 4, 0, 1, 4, 0, 2, 6, 0, 2, 6, 1, 4, 9, 1, 4, 9, 2, 6, 12, 2, 6, 13, 4, 9, 17, 4, 9, 18, 6, 12, 22, 6, 13, 24, 9, 17, 29, 9, 18, 31, 12, 22, 36, 13, 24, 39, 17, 29, 45, 18, 31, 48, 22, 36, 55, 24

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, 11, and 12. - Hoang Xuan Thanh, Apr 08 2026

Links

Table of n, a(n) for n=0..67.

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=0, a(6)=2, a(7)=0, a(8)=0, a(9)=2, a(10)=0, a(11)=1, a(12)=4, a(13)=0, a(14)=1, a(15)=4, a(16)=0, a(17)=2, a(18)=6, a(19)=0, a(20)=2, a(21)=6, a(22)=1, a(23)=4, a(24)=9, a(25)=1, a(26)=4, a(27)=9, a(28)=2, a(29)=6, a(30)=12, a(31)=2, a(n) = a(n - 3) + a(n - 6) - a(n - 9) + a(n - 11) + a(n - 12) - a(n - 14) - a(n - 15) - a(n - 17) - a(n - 18) + a(n - 20) + a(n - 21) - a(n - 23) + a(n - 26) + a(n - 29) - a(n - 32). - Harvey P. Dale, Jan 16 2013

a(n) = floor((2*n^3+30*n^2-489*n+6912)/28512 + ((n+2) mod 3)*(n^2+32*n)/432 - ((2*n^2+n) mod 3)*n*11/432 + (n/96)*(-1)^floor((n+2)/3) + ((6*n^3+2*n^2+7*n+1) mod 11)/11 + ((n^2+2) mod 3)/3). - Hoang Xuan Thanh, Apr 08 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^11)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Jan 16 2013 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A394017 A035461 A118508 * A339441 A226914 A110036

Adjacent sequences: A029302 A029303 A029304 * A029306 A029307 A029308

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved