This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065563 Product of three consecutive Fibonacci numbers. 11
 2, 6, 30, 120, 520, 2184, 9282, 39270, 166430, 704880, 2986128, 12649104, 53583010, 226980390, 961505790, 4073001576, 17253515288, 73087057560, 309601753890, 1311494059590, 5555578014142, 23533806080736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Mohammad K. Azarian, Fibonacci Identities as Binomial Sums II, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 42, 2012, pp. 2053-2059. Mohammad K. Azarian, Fibonacci Identities as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 38, 2012, pp. 1871-1876. T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, 2001, p. 89, No. 32, with a minus sign. LINKS Harry J. Smith, Table of n, a(n) for n=1..200 V. E. Hoggatt, D. A. Lind, The Heights of Fibonacci Polynomials and an Associated Function, Fibonacci Quarterly, 5;2, April, 1967, pp. 141-152. Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1). FORMULA a(n) = A000045(n)*A000045(n+1)*A000045(n+2). G.f.: 2/(1 - 3*x - 6*x^2 + 3*x^3 + x^4). a(n) = 2*A001655(n). a(n) = Fibonacci(n+1)^3-(-1)^n*Fibonacci(n+1). - Gary Detlefs, Feb 02 2011 This corrects a sign mistake in the Koshy reference. - Wolfdieter Lang, Aug 07 2012 a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4). O.g.f.: 2*x/((1 + x - x^2)*(1 - 4*x - x^2)) (compare with A001655). - Wolfdieter Lang, Aug 06 2012 MAPLE with (combinat):a:=n->fibonacci(n)*fibonacci(n+1)*fibonacci(n+2): seq(a(n), n=1..22); # Zerinvary Lajos, Oct 07 2007 MATHEMATICA fib[n_]:=If[n==1||n==2, 1, fib[n-1]+fib[n-2]]; a={}; Do[f1=fib[n]; f2=fib[n+1]; f3=fib[n+2]; p=f1*f2*f3; AppendTo[a, p], {n, 1, 20}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *) Times@@@Partition[Fibonacci[Range[30]], 3, 1] (* Harvey P. Dale, Aug 18 2011 *) PROG (PARI) { for (n=1, 200, a=fibonacci(n)*fibonacci(n + 1)*fibonacci(n + 2); write("b065563.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 22 2009 CROSSREFS Cf. A000045, A001655. Sequence in context: A071760 A304579 A036752 * A035105 A073969 A295863 Adjacent sequences:  A065560 A065561 A065562 * A065564 A065565 A065566 KEYWORD nonn,easy AUTHOR Len Smiley, Nov 30 2001 EXTENSIONS Offset changed from 0 to 1 by Harry J. Smith, Oct 22 2009 STATUS approved

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

Last modified September 16 12:40 EDT 2019. Contains 327112 sequences. (Running on oeis4.)