# [seqfan] Re: sequence challenge

Alois Heinz heinz at hs-heilbronn.de
Mon Nov 21 20:56:29 CET 2011

```It seems that there are more examples:

a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|5>>^n)[1, 1]:

gives: 1, 0, 0, 1, 5, 24, 116, 561, 2713, 13120, 63448, 306833, 1483837,
7175800, 34701996, 167818017
G.f.: (-x^2+5*x-1)/(x^3-x^2+5*x-1)

(not in OEIS)

The sum of the absolute values of matrix elements is 9 here.
Is there a smaller example w.r.t. this measure?

Alois

Am 21.11.2011 20:19, schrieb israel at math.ubc.ca:
> My first try worked:
>
> M = [[2, -1, 2], [-1, 0, 1], [1, 2, 0]]
>
> Sequence (M^n)[1,1] is
>
> 1, 2, 7, 15, 47, 106, 312, 731, 2068, 4983, 13727, 33757, 91302,
> 227846, 608389, 1534290, 4059911, 10315771, 27122487, 69284630,
> 181339756, ...
>
> It has generating function (1-2*t^2)/(1-2*t-5*t^2+9*t^3)
>
> Robert Israel                                israel at math.ubc.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia            Vancouver, BC, Canada
>

```