A029348 Expansion of 1/((1-x^4)*(1-x^6)*(1-x^7)*(1-x^9)).

1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 5, 4, 6, 6, 6, 7, 8, 7, 9, 9, 10, 10, 12, 11, 14, 13, 14, 15, 17, 16, 19, 19, 20, 21, 23, 22, 26, 26, 27, 28, 31, 30, 34, 34, 36, 37, 40, 39, 44, 44, 46, 48, 51

Offset

0,13

Comments

Number of partitions of n into parts 4, 6, 7, and 9. - Hoang Xuan Thanh, May 09 2026

Links

Table of n, a(n) for n=0..64.

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

Formula

a(n) = floor((n^3+39*n^2+612*n+6480)/9072 - (n mod 2)*n/48 - ((2*n^2+n) mod 3)*n/54 + ((6*n^3+3*n^2+4*n+2) mod 7)/7). - Hoang Xuan Thanh, May 09 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^6)(1-x^7)(1-x^9)), {x, 0, 70}], x] (* Harvey P. Dale, Nov 24 2017 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 1, 0, 1, 1, 0, 1, -1, -1, 0, -2, 0, -1, -1, 1, 0, 1, 1, 0, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 5, 4, 6, 6}, 70] (* Harvey P. Dale, Nov 24 2017 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^6)*(1-x^7)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Sequence in context: A293223 A391109 A361514 * A070093 A174931 A058744

Adjacent sequences: A029345 A029346 A029347 * A029349 A029350 A029351

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved