A029138 Expansion of 1/((1-x^2)(1-x^3)(1-x^4)(1-x^8)).

1, 0, 1, 1, 2, 1, 3, 2, 5, 3, 6, 5, 9, 6, 11, 9, 15, 11, 18, 15, 23, 18, 27, 23, 34, 27, 39, 34, 47, 39, 54, 47, 64, 54, 72, 64, 84, 72, 94, 84, 108, 94, 120, 108, 136, 120, 150, 136, 169, 150, 185, 169, 206, 185, 225, 206, 249, 225, 270, 249, 297, 270, 321, 297, 351, 321

Offset

0,5

Comments

Number of partitions of n into parts 2, 3, 4, and 8. - Joerg Arndt, Jul 07 2013

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((2*n^3 + 51*n^2 + 387*n + 1665 + 9*((n^2+17*n+63) + 8*(floor(n/2)+1)*(-1)^floor(n/2))*(-1)^n)/2304). - Tani Akinari, Jul 07 2013

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^4)(1-x^8)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^8))+O(x^66)) \\ Joerg Arndt, Jul 07 2013

Crossrefs

Sequence in context: A348112 A045747 A308984 * A161051 A161255 A008731

Adjacent sequences: A029135 A029136 A029137 * A029139 A029140 A029141

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved