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Maple can't find linear recurrence

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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]

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Maple can't find linear recurrence Peter Luschny <peter.luschny@gmail.com> - 2017-10-09 08:20 -0700
  Re: Maple can't find linear recurrence "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2017-10-12 04:33 -0600
    Re: Maple can't find linear recurrence Thomas Richard <trichard@maplesoft.com> - 2017-10-13 00:14 -0700
      Re: Maple can't find linear recurrence Peter Luschny <peter.luschny@gmail.com> - 2017-10-17 12:42 -0700
        Re: Maple can't find linear recurrence "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2017-10-18 07:59 -0600
          Re: Maple can't find linear recurrence Peter Luschny <peter.luschny@gmail.com> - 2017-10-20 04:15 -0700
            Re: Maple can't find linear recurrence Axel Vogt <//noreply@axelvogt.de> - 2017-10-20 21:13 +0200

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