A029308 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^11)).

1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 2, 3, 3, 3, 3, 4, 5, 4, 5, 6, 5, 6, 7, 7, 8, 8, 9, 10, 9, 11, 12, 11, 13, 14, 14, 15, 16, 17, 18, 18, 20, 21, 21, 23, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 40, 42, 43, 45

Offset

0,12

Comments

Number of partitions of n into parts 3, 7, 8, and 11. - Hoang Xuan Thanh, Apr 09 2026

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((1414*n^3+1029*n^2+1596*n+2986)/2016) - floor((3*n^3+n^2+2*n+4)/7) - floor((3*n^3+4*n^2+5*n+10)/11). - Hoang Xuan Thanh, Apr 09 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^8)(1-x^11)), {x, 0, 70}], x] (* Harvey P. Dale, May 11 2019 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 09 2026

Crossrefs

Sequence in context: A234567 A241950 A316776 * A218879 A340381 A029259

Adjacent sequences: A029305 A029306 A029307 * A029309 A029310 A029311

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved