[seqfan] Re: Duplicated "A*x+B" sequences
mathar at strw.leidenuniv.nl
Mon Nov 30 21:05:55 CET 2009
jol> Return-Path: <seqfan-bounces at list.seqfan.eu>
jol> Date: Mon, 30 Nov 2009 20:21:56 +0100
jol> From: Jaume Oliver i Lafont <joliverlafont at gmail.com>
jol> To: seqfan at list.seqfan.eu
jol> Subject: [seqfan] Re: Duplicated "A*x+B" sequences
jol> sequences with
jol> also have
jol> Subtracting these equations, the (simpler?) recurrence
jol> is obtained.
jol> Moreover, since
jol> all of them satisfy the fourth-order linear recurrence
jol> This is written as (0,2,0,-1) in the OEIS index for linear recurrences
The recurrences in these cases are of third order after
elimination of any constant term, as demonstrated in
A168195, A168202 or A168212.
So the entries in Sindx_Rea.html#recLCC would refer to the
form equivalent to the denominator (1+x)(1-x)^2 with a third order
degree of the polynomial, namely (1,1,-1), not to the 4-th order (0,2,0,-1) , because
the index associates sequences with the recurrences of smallest polynomial degree.
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