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A065563
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Product of three consecutive Fibonacci numbers.
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14
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: 2/(1 - 3*x - 6*x^2 + 3*x^3 + x^4).
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).
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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, Oct 07 2007
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MATHEMATICA
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Times@@@Partition[Fibonacci[Range[30]], 3, 1] (* Harvey P. Dale, Aug 18 2011 *)
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PROG
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(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
(Magma) [&*[Fibonacci(n+k): k in [0..2] ]: n in [1..30]]; // Vincenzo Librandi, Apr 09 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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