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Search: id:A065563
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| A065563 |
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Product of three consecutive Fibonacci numbers. |
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+0
4
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| 2, 6, 30, 120, 520, 2184, 9282, 39270, 166430, 704880, 2986128, 12649104, 53583010, 226980390, 961505790, 4073001576, 17253515288, 73087057560, 309601753890, 1311494059590, 5555578014142, 23533806080736
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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V. E. Hoggatt, D. A. Lind, "The Heights of Fibonacci Polynomials and an Associated Function", Fibonacci Quarterly, 5;2, April, 1967, pp. 141-152.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
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a(n)=A000045(n)*A000045(n+1)*A000045(n+2). G.f.: 2/(1-3*x-6*x^2+3*x^3+x^4)
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MAPLE
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with (combinat):a:=n->fibonacci(n)*fibonacci(n+1)*fibonacci(n+2): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
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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 Orlovsky, Jul 22 2008)
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PROGRAM
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(PARI) { for (n=1, 200, a=fibonacci(n)*fibonacci(n + 1)*fibonacci(n + 2); write("b065563.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 22 2009]
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CROSSREFS
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Cf. A000045
Equals 2 * A001655(n).
Sequence in context: A071758 A071760 A036752 this_sequence A035105 A073969 A120950
Adjacent sequences: A065560 A065561 A065562 this_sequence A065564 A065565 A065566
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KEYWORD
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nonn
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 30 2001
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EXTENSIONS
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OFFSET changed from 0,1 to 1,1 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 22 2009
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