A029173 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^5)*(1-x^8)).

1, 0, 1, 0, 2, 1, 2, 1, 4, 2, 5, 2, 7, 4, 8, 5, 11, 7, 13, 8, 17, 11, 19, 13, 24, 17, 27, 19, 33, 24, 37, 27, 44, 33, 49, 37, 57, 44, 63, 49, 73, 57, 80, 63, 91, 73, 99, 80, 112, 91, 122, 99, 136, 112, 147, 122, 163, 136, 176, 147, 194, 163, 208, 176, 228, 194, 244, 208

Offset

0,5

Comments

Number of partitions of n into parts 2, 4, 5, and 8. - Hoang Xuan Thanh, Oct 08 2025

Links

Table of n, a(n) for n=0..67.

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

Formula

a(n) = floor((n^3+36*n^2+416*n+1920)/1920 - (n^2+19*n+55)*(n mod 2)/128 - n*((n^2+3*n) mod 4)/64). - Hoang Xuan Thanh, Oct 08 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^5)(1-x^8)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 15 2020 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^5)*(1-x^8)) + O(x^68)) \\ Hoang Xuan Thanh, Oct 08 2025

Crossrefs

Sequence in context: A029196 A051493 A338201 * A002331 A060805 A184342

Adjacent sequences: A029170 A029171 A029172 * A029174 A029175 A029176

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Hoang Xuan Thanh, Oct 08 2025

Status

approved