A029366 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^10)*(1-x^11)).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 1, 3, 2, 2, 3, 4, 2, 3, 4, 4, 3, 5, 5, 5, 5, 7, 6, 6, 7, 8, 7, 8, 9, 10, 9, 11, 11, 12, 11, 13, 13, 14, 14, 16, 16, 17, 17, 19, 19, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30

Offset

0,12

Comments

Number of partitions of n into parts 4, 7, 10, and 11. - Hoang Xuan Thanh, Jun 19 2026

Links

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

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

Formula

a(n) = floor((n^3+48*n^2+812*n-7824)/18480 - (n mod 2)*n/80 + ((6*n^3+n^2+5) mod 7)/7 + ((4*n^3+5*n^2+3*n+10) mod 11)/11). - Hoang Xuan Thanh, Jun 19 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^7)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 19 2026
(Python)
from sympy import Matrix
def A029366(n):
    A = Matrix([1]+[0]*31)*Matrix([0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1]).T+Matrix(32, 32, lambda i, j: int(i-j==1))
    return (A**n*Matrix([1]+[0]*31))[0] # Chai Wah Wu, Jun 19 2026

Crossrefs

Sequence in context: A113423 A131258 A298596 * A260945 A255648 A112848

Adjacent sequences: A029363 A029364 A029365 * A029367 A029368 A029369

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved