# [seqfan] Re: sequence challenge

israel at math.ubc.ca israel at math.ubc.ca
Mon Nov 21 20:19:42 CET 2011

```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

On Nov 21 2011, Alois Heinz wrote:

>
>a:= n-> (<<0|1|0>,
><0|0|1>,
><1|-3|5>> ^n)[1,1];
>gives: 1, 0, 0, 1, 5, 22, 96, 419, 1829, 7984, 34852, 152137, 664113,
>2899006, 12654828, 55241235
>
>is not in the OEIS.
>
>Alois
>
>Am 21.11.2011 18:02, schrieb Peter Lawrence:
>>
>> an odd story: I was trying to find a 3x3 matrix for Tri-bonacci numbers
>> like the [[1,0][1,1]]**n for generating Fibonacci numbers, and finally
>> figured one out through logic. I initially thought I would find one by
>> trial-and-error, but that didn't work for me. Here's the odd part, all
>> the trial-and-error matricies I tried did end up matching something in
>> the OEIS !
>>
>> so here is the challenge, find a 3x3 integer matrix with "smallish"
>> elements whose powers generate a sequence that is _not_ in the OEIS.
>>
>> (taking the [0,0]'th element of each matrix as the sequence).
>>
>>
>> -Peter Lawrence.
>>
>
>
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>

```