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Newsgroups: comp.soft-sys.math.maple
Date: Mon, 9 Oct 2017 08:20:51 -0700 (PDT)
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Subject: Maple can't find linear recurrence
From: Peter Luschny <peter.luschny@gmail.com>
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Xref: csiph.com comp.soft-sys.math.maple:1265

restart: with(gfun):

L := [1,2,5,8,13,18,25,31,41,49,61,71,85,97,113,126, 145,160,181,198,221,240,265,285,313,335,365,389,421, 447,481,508,545,574,613,644,685,718]:
rec := listtorec(L, u(n));

# Maple fails immediately, although there is a linear recurrence:

recS := {-a(n)+2*a(n+2)-a(n+4)+a(n+8)-2*a(n+10)+a(n+12),a(0)=1,a(1)=2,a(2)=5, a(3)=8,a(4)=13,a(5)=18,a(6)=25,a(7)=31,a(8)=41,a(9)=49,a(10)=61,a(11)=71};
r := rectoproc(recS, a(n), remember):
seq(r(n), n=0..150);

# I found this recurrence of order 12 'by hand'. Mathematica's 
# FindLinearRecurrence found this recurrence of order 11 from
# the same data:

# LinearRecurrence[ {1,1,-1,0,0,0,0,1,-1,-1,1} , 
# {1, 2, 5, 8, 13, 18, 25, 31, 41, 49, 61}, 150]