[seqfan] Re: sequence challenge

Ed Jeffery ed.jeffery at yahoo.com
Wed Nov 23 02:36:50 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


Alois, it looks like this is another one:

Let M=[(0,1,0);(1,0,1);(0,1,5)], then 

{[M^n]_(0,0)}={1,0,1,0,2,5,29,145,758,3935,20466,...}, 

n=0,1,2,..., with irreducible 

g.f.: (1-5*x-x^2)/(1-5*x-2*x^2+5*x^3)

and not in OEIS. Is this "smaller" according to your 

definition? It seems to be term-wise smaller than your
sequence, if that is relevant.

Ed Jeffery


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