A025816 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^8)).

1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 2, 4, 2, 4, 3, 5, 4, 6, 4, 6, 4, 7, 5, 8, 6, 9, 6, 9, 7, 10, 8, 11, 9, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 21, 17, 22, 18, 23, 19, 24, 21, 26, 22, 27

Offset

0,9

Comments

Number of partitions of n into parts 2, 7, and 8. - Hoang Xuan Thanh, Aug 30 2025

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^2 + 17*n + 168 + 7*(n+9)*(-1)^n +19*( ((n+2) mod 7) - (n mod 7) )) /224). - Hoang Xuan Thanh, Aug 30 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^7)(1-x^8)), {x, 0, 70}], x] (* Harvey P. Dale, Jun 05 2018 *)
(* Alternative: *)
LinearRecurrence[{0, 1, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4}, 70] (* Harvey P. Dale, Jun 05 2018 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^7)*(1-x^8)) + O(x^75)) \\ Jinyuan Wang, Feb 28 2020
(PARI) a(n) = (n^2 +17*n +168 +7*(n+9)*(-1)^n +19*((n+2)%7-n%7)) \224 \\ Hoang Xuan Thanh, Aug 30 2025

Crossrefs

Sequence in context: A008622 A029414 A053275 * A025813 A161231 A161055

Adjacent sequences: A025813 A025814 A025815 * A025817 A025818 A025819

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved