FW: A101368

[Max A.]

On 8/1/06, Floor en Lyanne van Lamoen <fvanlamoen at planet.nl> wrote:
> Dear all,
>
> The sequence A101368 seems to follow the recursions
>
> a(n) = 6a(n-1)-6a(n-2)+a(n-3)
> a(n) = 5a(n-1)-a(n-2)-1
>
> Is there a good reason for this?

That follows from the formula
a(n) = 2 * A089817(n-3) + 1, n>2. - Ralf Stephan, Jan 14 2005
and the generating function for A089817:
%F A089817 G.f.: 1/((1-x)*(1-5*x+x^2)) = 1/(1-6*x+6*x^2-x^3).

Max