[seqfan] Re: A new sequence

Maximilian Hasler maximilian.hasler at gmail.com
Tue Feb 5 20:41:07 CET 2013


> Wikipedia says a "characteristic polynomial" is connected to a matrix.
> Do you use the matrix to generate the sequence (and of so, how)?

Here, that one is meant:

http://en.wikipedia.org/wiki/Recurrence_relation#Linear_homogeneous_recurrence_relations_with_constant_coefficients

although both notions can be linked...

> I guess the more general question is: Do you have software that can
> automatically generate the 1000 or so divisibility sequences?

Here, a script which appends n values to
the r initial values  of a lin.rec. of order r,
already helps:

(PARI)
{linrec(c,a,n=10)=for(k=1,n,a=concat(a,-vecextract(a,Str(-#c,".."))*c~));a}

linrec([1,-40,206,-40],[1,0,1,48])

=> [1, 0, 1, 48, 1713, 58672, 1995921, 67818880, 2303940641,
78266714528, 2658767568353, 90319849348112, 3068216219484241,...]
\\ NOT IN OEIS ;
 but since highly composite, it is quite probable that it is the
product of two or more sequences in the OEIS

gp > linrec([1,-40,206,-40],[-1,0,1,6])
=>
-1, 0, 1, 6, 35, 204, 1189, 6930, 40391, 235416, 1372105, 7997214,
46611179, 271669860,...
\\ this is A001109

gp > linrec([1,-40,206,-40],[-1,0,1,34])
 =>
-1, 0, 1, 34, 1155, 39236, 1332869, 45278310, 1538129671, 52251130504,
1775000307465, 60297759323306, ...

\\this is A091761 (from the 0 on) resp. A029547 (from the 1 on)

gp > linrec([1,-40,206,-40],[-1,0,1,48])
 ms.
-1, 0, 1, 48, 1715, 58752, 1998709, 67914000, 2307174311, 78376578048,
2662499775145, 90446634986352,

\\ NOT in the OEIS, but same remark as above.

Maximilian


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