A029107 Expansion of 1/((1-x)*(1-x^6)*(1-x^7)*(1-x^9)).

1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 6, 7, 8, 9, 9, 11, 12, 13, 15, 16, 17, 19, 21, 22, 25, 27, 28, 31, 33, 35, 38, 41, 43, 47, 50, 52, 56, 59, 62, 67, 71, 74, 79, 83, 86, 92, 97, 101, 107, 112, 116, 123, 129, 134, 141

Offset

0,7

Comments

Number of partitions of n into parts 1, 6, 7 and 9. - Hoang Xuan Thanh, Jul 23 2025

Links

Table of n, a(n) for n=0..57.

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

Formula

a(n) = floor((2*n^3 + 69*n^2 + 738*n + 5103)/4536 - (n/54)*[(n mod 3)=2] - (1/3)*[(n mod 7) in {3,4,5}]). - Hoang Xuan Thanh, Jul 23 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^6)(1-x^7)(1-x^9)), {x, 0, 70}], x] (* Jinyuan Wang, Mar 18 2020 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0, 0, -1, 1, -1, 0, 1, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 6, 7, 8, 9, 9, 11, 12, 13, 15, 16}, 80] (* Harvey P. Dale, Apr 22 2022 *)

Crossrefs

Sequence in context: A048182 A300293 A316388 * A209727 A063123 A086333

Adjacent sequences: A029104 A029105 A029106 * A029108 A029109 A029110

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved