A029151 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^8)).

1, 0, 1, 1, 1, 1, 3, 1, 4, 3, 4, 4, 7, 4, 9, 7, 10, 9, 14, 10, 17, 14, 19, 17, 25, 19, 29, 25, 32, 29, 40, 32, 46, 40, 50, 46, 60, 50, 68, 60, 74, 68, 86, 74, 96, 86, 104, 96, 119, 104, 131, 119, 141, 131, 159, 141, 174

Offset

0,7

Comments

Number of partitions of n into parts 2, 3, 6 and 8. - Hoang Xuan Thanh, Jul 10 2025

Links

Table of n, a(n) for n=0..56.

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

Formula

a(2*n) = a(2*n+3) = floor((2*n^3 + 33*n^2 + 180*n + 432)/432 - ((n+1)/9)*[(n mod 3)=2]). - Hoang Xuan Thanh, Jul 11 2025

a(n) = floor((n^3+33*n^2+360*n+1728)/1728 - (n^2+19*n)*(n mod 2)/192 - (n+6)*((2*n^2+2*n) mod 3)/18). - Hoang Xuan Thanh, Oct 03 2025

Mathematica

CoefficientList[Series[ 1/((1-x^2)(1-x^3)(1-x^6)(1-x^8)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 1, 0, 0, -1, -1, 0, 0, 1, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 3, 1, 4, 3, 4, 4, 7, 4, 9, 7, 10, 9, 14}, 100] (* Harvey P. Dale, Jun 04 2021 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^8)) + O(x^90)) \\ Jinyuan Wang, Mar 18 2020
(PARI) a(n) = {my(m = (2*n - 3 + 3*(-1)^n)/4); floor((2*m^3 + 33*m^2 + 180*m + 432)/432 - (m+1)/9*(m%3==2))} \\ Hoang Xuan Thanh, Jul 10 2025

Crossrefs

Sequence in context: A339106 A082909 A335906 * A102595 A113415 A332801

Adjacent sequences: A029148 A029149 A029150 * A029152 A029153 A029154

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved