A029181 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^8)).

1, 0, 1, 0, 2, 0, 2, 1, 4, 1, 4, 2, 6, 2, 7, 4, 10, 4, 11, 6, 14, 7, 16, 10, 20, 11, 22, 14, 27, 16, 30, 20, 36, 22, 39, 27, 46, 30, 50, 36, 58, 39, 63, 46, 72, 50, 78, 58, 88, 63, 95, 72, 106, 78, 114, 88, 127, 95, 136, 106

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 7, and 8. - Hoang Xuan Thanh, Oct 11 2025

Links

Table of n, a(n) for n=0..59.

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

Formula

a(n) = floor((n^3+42*n^2+476*n+3072)/2688 - (n^2+21*n+58)*(n mod 2)/128 + n*((n^2+n+2) mod 4)/64). - Hoang Xuan Thanh, Oct 11 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^7)(1-x^8)), {x, 0, 70}], x] (* Harvey P. Dale, May 07 2011 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^8)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A278648 A353508 A382117 * A261426 A260574 A058707

Adjacent sequences: A029178 A029179 A029180 * A029182 A029183 A029184

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved