A029258 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^7)*(1-x^9)).

1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 5, 4, 6, 6, 6, 8, 8, 8, 10, 11, 10, 13, 14, 13, 16, 17, 17, 19, 21, 21, 24, 25, 25, 29, 30, 30, 34, 36, 36, 40, 42, 42, 47, 49, 49, 54, 57, 57, 62, 65, 66, 71, 74, 75, 81, 84

Offset

0,8

Comments

Number of partitions of n into parts 3, 4, 7, and 9. - Vincenzo Librandi, Jun 03 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((2*n^3+69*n^2+828*n+3888)/9072 - ((2*n^2+n) mod 3)*n/27 + ((5*n^3+n^2+5*n+4) mod 7)/7). - Hoang Xuan Thanh, Mar 22 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^7) (1 - x^9)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)
LinearRecurrence[{0, 0, 1, 1, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1}, {1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 5, 4, 6, 6, 6, 8, 8}, 70] (* Harvey P. Dale, Oct 21 2025 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^7)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A232194 A054705 A025800 * A280128 A367055 A354703

Adjacent sequences: A029255 A029256 A029257 * A029259 A029260 A029261

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved