A025797 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^8)).

1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 11, 9, 12, 11, 13, 12, 15, 13, 17, 15, 18, 17, 20, 18, 22, 20, 24, 22, 26, 24, 28, 26, 30, 28, 33, 30, 35, 33, 37, 35, 40, 37, 43, 40, 45, 43, 48, 45, 51, 48, 54, 51, 57, 54, 60, 57, 63, 60

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, and 8. - Hoang Xuan Thanh, Jun 16 2025

Links

Table of n, a(n) for n=0..71.

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

Formula

a(n) = a(n-2)+a(n-3)-a(n-5)+ a(n-8)- a(n-10)- a(n-11)+a(n-13), a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=1, a(8)=3, a(9)=2, a(10)=3, a(11)=3, a(12)=4, - Harvey P. Dale, Sep 28 2012

a(n) = floor((n^2 + (13+3*(-1)^n)*n + 77 + 19*(-1)^n)/96). - Hoang Xuan Thanh, Jun 16 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^8)), {x, 0, 70}], x] (* Harvey P. Dale, Sep 28 2012 *)
(* Alternative: *)
LinearRecurrence[{0, 1, 1, 0, -1, 0, 0, 1, 0, -1, -1, 0, 1}, {1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 4}, 70] (* Harvey P. Dale, Sep 28 2012 *)

Crossrefs

Sequence in context: A317243 A051274 A267806 * A035386 A244327 A319318

Adjacent sequences: A025794 A025795 A025796 * A025798 A025799 A025800

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved