The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A059840 a(n) = F(n)*F(n-1) if n odd otherwise F(n)*F(n-1)-1, where F = Fibonacci numbers A000045. 15
 0, 0, 2, 5, 15, 39, 104, 272, 714, 1869, 4895, 12815, 33552, 87840, 229970, 602069, 1576239, 4126647, 10803704, 28284464, 74049690, 193864605, 507544127, 1328767775, 3478759200, 9107509824, 23843770274, 62423800997, 163427632719 (list; graph; refs; listen; history; text; internal format)
 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*A001654(n) + A027941(n))/2, n >= 0. - Wolfdieter Lang, Jul 21 2012 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 For n > 2, 2 * A000217(a(n)) = A228873(n-2). - Diego Rattaggi, Jan 27 2021 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 Cf. A000045, A001654, A059248, A064831, A119996. Sequence in context: A148341 A258121 A242823 * A280064 A148342 A148343 Adjacent sequences: A059837 A059838 A059839 * A059841 A059842 A059843 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 26 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 3 10:55 EDT 2023. Contains 365861 sequences. (Running on oeis4.)