[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
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