OFFSET
1,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..500
S. Falcon, On the Sequences of Products of Two k-Fibonacci Numbers, American Review of Mathematics and Statistics, March 2014, Vol. 2, No. 1, pp. 111-120.
H. Ohtsuka and S. Nakamura, On the sum of reciprocal sums of Fibonacci numbers, Fibonacci Quart. 46/47 (2008/2009), 153-159.
FORMULA
G.f.: (x^3)*(2-x)/((1-x^2)*(1-3*x+x^2)), with a(0):=0. See a comment on A080144. - Wolfdieter Lang, Jul 30 2012
a(n) = Sum_{k=1..n-2} F(k)*F(k+2). - Alexander Adamchuk, May 17 2007
a(n+2) = (3*(-1)^(n+1) - 5 + 2*Lucas(2*n + 3))/10, n >= 0. - Ehren Metcalfe, Aug 21 2017
a(n) = floor(1/(Sum_{k>=n} 1/Fibonacci(k)^2)) [Ohtsuka and Nakamura]. - Michel Marcus, Aug 09 2018
MAPLE
seq(coeff(series(x^3*(2-x)/((1-x^2)*(1-3*x+x^2)), x, n+1), x, n), n=1..30); # Muniru A Asiru, Aug 09 2018
MATHEMATICA
Table[If[OddQ[n], Fibonacci[n]Fibonacci[n-1], Fibonacci[n] Fibonacci[n-1]-1], {n, 30}] (* Harvey P. Dale, Apr 20 2011 *)
PROG
(PARI) { b=0; f=1; for (n=1, 500, a=f*b; if (frac(n/2)==0, a--); write("b059840.txt", n, " ", a); a=f + b; b=f; f=a; ) } \\ Harry J. Smith, Jun 29 2009
(GAP) List([1..30], n->Sum([1..n-2], k->Fibonacci(k)*Fibonacci(k+2))); # Muniru A Asiru, Aug 09 2018
(Magma) F:=Fibonacci; [(n mod 2) eq 0 select F(n)*F(n-1)-1 else F(n)*F(n-1): n in [1..30]]; // G. C. Greubel, Jul 23 2019
(Sage) a=(x^3*(2-x)/((1-x^2)*(1-3*x+x^2))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jul 23 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 26 2001
STATUS
approved