[PURRS-devel] problem with PURRS ? - with regards to OEIS's A136429

[Alexander Povolotsky]

x(n-1) + x(n-2) + x(n-3)
x(0) = 1; x(1) = 1; x(2) = 1

PURRS output "memory limit exceeded"

On Sun, Apr 6, 2008 at 8:50 PM, Alexander Povolotsky <apovolot at gmail.com> wrote:
> x(n)=x(n-x(n-1))+x(n-x(n-2))
>
>  PURRS output "this recurrence is malformed"
>
>
>
>  On Sat, Apr 5, 2008 at 10:27 PM, Alexander Povolotsky
>  <apovolot at gmail.com> wrote:
>  > Hi,
>  >
>  >  Here is the OEIS sequence description:
>  >  A136429
>  >  a(n) = sum( F(k+1)^2 F(n-k+1)^2, k = 0..n ) where F(n) = Fibonacci
>  >  number (A000045).
>  >
>  >         1, 2, 9, 26, 84, 250, 747, 2182, 6323, 18132, 51624, 146004, 410677,
>  >  1149578, 3204477, 8899502, 24634620, 67990414, 187154271, 513939214,
>  >  1408246247, 3851081256, 10512259920, 28647203880, 77946605545,
>  >  211782868754
>  >
>  >  OFFSET
>  >
>  >  0,2
>  >
>  >  FORMULA
>  >
>  >  G.f.: (1-x)^2/((1+x)^2(1-3x+x^2)^2).
>  >
>  >   Recurrence: a(n+6) = 4 a(n+5) - 10 a(n+3) + 4 a(n+1) - a(n).
>  >
>  >  AUTHOR
>  >
>  >  Emanuele Munarini (emanuele.munarini(AT)polimi.it), Apr 01 2008
>  >
>  >  So I tried PURRS
>  >  http://www.cs.unipr.it/purrs/
>  >  PURRS Demo Results
>  >  Exact solution for x(n) = -x(6+n)+4*x(5+n)-10*x(3+n)+4*x(1+n)
>  >  for the initial conditions
>  >  x(0) = 1
>  >  x(1) = 2
>  >  x(2) = 9
>  >  x(3) = 26
>  >  x(4) = 84
>  >  x(5) = 250
>  >  x(n) = -(-1)^n*n-2/5*(3/2+1/2*sqrt(5))^n+9/5*(-1)^n+4/5*(3/2+1/2*sqrt(5))^n*sqrt(5)-4/5
>  >  *(3/2-1/2*sqrt(5))^n*sqrt(5)-2/5*(3/2-1/2*sqrt(5))^n
>  >  for each n >= 0
>  >  Then I have defined sequence in PARI using close formula generated by PURRS
>  >  (21:16) gp > a(n)=-(-1)^n*n-2/5*(3/2+1/2*sqrt(5))^n+9/5*(-1)^n+4/5*(3/2+1/2*sqrt(5))^n*sqrt(5)-4/5
>  >  *(3/2-1/2*sqrt(5))^n*sqrt(5)-2/5*(3/2-1/2*sqrt(5))^n
>  >
>  >  But it doesn't even give initial conditions ... ?
>  >  (21:16) gp > a(0)
>  >  %5 = 1.000000000000000000000000000
>  >  (21:16) gp > a(1)
>  >  %6 = 2.000000000000000000000000000
>  >  (21:17) gp > a(3)
>  >  %7 = 26.00000000000000000000000000
>  >  (21:17) gp > a(4)
>  >  %8 = 63.00000000000000000000000000
>  >  (21:17) gp > a(5)
>  >  %9 = 174.0000000000000000000000000
>  >  (21:19) gp > a(6)
>  >  %10 = 443.0000000000000000000000000
>  >
>  >  Did I make a mistake in above or ... ?
>  >
>  >  Ciao,
>  >  Regards,
>  >  Alex
>  >
>