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

Alexander Povolotsky apovolot at gmail.com
Sun Apr 6 04:27:49 CEST 2008

```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

```