A029306 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^9)).

1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 3, 3, 4, 3, 3, 5, 4, 5, 7, 6, 6, 8, 7, 7, 10, 9, 10, 12, 11, 12, 14, 13, 14, 17, 16, 17, 20, 19, 20, 23, 22, 23, 27, 26, 27, 31, 30, 31, 35, 34, 36, 40, 39, 41, 45, 44, 46, 51, 50

Offset

0,10

Comments

Number of partitions of n into parts 3, 7, 8, and 9. - Hoang Xuan Thanh, Apr 09 2026

Links

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

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

Formula

a(n) = floor((2*n^3+81*n^2+768*n+10272)/18144 + ((2*n^2+1) mod 3)*(n+4)/27 + ((6*n^3+5*n^2+n+2) mod 7)/7 - 10*(n mod 3)/81). - Hoang Xuan Thanh, Apr 09 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^8)(1-x^9)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 0, 1, 1, 1, -1, -1, -1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 3, 3, 4, 3, 3, 5, 4, 5, 7, 6, 6}, 70] (* Harvey P. Dale, Jun 07 2016 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^8)*(1-x^9)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 09 2026

Crossrefs

Sequence in context: A161106 A161041 A153907 * A337511 A261363 A341216

Adjacent sequences: A029303 A029304 A029305 * A029307 A029308 A029309

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved