A029330 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^11)).

1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 3, 4, 3, 3, 3, 5, 5, 6, 5, 6, 6, 8, 8, 9, 8, 10, 10, 12, 12, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 24, 24, 26, 26, 29, 29, 32, 32, 35, 35, 38, 39, 42, 42, 45, 46, 50, 50, 53, 54

Offset

0,11

Comments

Number of partitions of n into parts 4, 5, 6, and 11. - Hoang Xuan Thanh, Apr 17 2026

Links

Table of n, a(n) for n=0..63.

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

Formula

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

a(n) = floor((n^3+39*n^2+540*n+2535)/7920 - (n mod 2)*(n+14)/48 + ((2*n^3+n^2+2*n+10) mod 11)/11). - Hoang Xuan Thanh, Apr 17 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^6)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[ {0, 0, 0, 1, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 3, 4, 3, 3, 3, 5, 5, 6, 5, 6, 6}, 80] (* Harvey P. Dale, Jul 10 2013 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^6)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 17 2026

Crossrefs

Sequence in context: A297030 A266348 A179647 * A132225 A263923 A331248

Adjacent sequences: A029327 A029328 A029329 * A029331 A029332 A029333

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved