close form solution for A136010 (per PURRS http://www.cs.unipr.it/purrs/)

[Max Alekseyev]

On Sat, Mar 29, 2008 at 11:35 AM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:

>  Maple:
>  A136010:=n->simplify((10+61/sqrt(85))*(7/2-1/2*sqrt(85))^n+(10-61/sqrt(85))*(7/2+1/2*sqrt(85))^n);
>
>  PARI:
>  A136010(n) = round((10+61/sqrt(85))*(7/2-1/2*sqrt(85))^n+(10-61/sqrt(85))*(7/2+1/2*sqrt(85))^n)

The latter is not that good since sqrt() in PARI is not precise but
floating-point function (in contrast to Maple, where it is symbolic by
default). Therefore, this function may give wrong results for large n
or an error like:

  *** round: precision too low in truncr (precision loss in truncation).

In PARI it is better to use the following code that does not involve
any floating point operations:

A136010(n) = local(y=Mod(x,x^2-85));
lift((10+61/y)*(7/2-1/2*y)^n+(10-61/y)*(7/2+1/2*y)^n)

Regards,
Max