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A059727
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a(n) = Fibonacci(n)*(Fibonacci(n) + 1).
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5
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0, 2, 2, 6, 12, 30, 72, 182, 462, 1190, 3080, 8010, 20880, 54522, 142506, 372710, 975156, 2552006, 6679640, 17484942, 45771990, 119825862, 313697232, 821252306, 2150037792, 5628825650, 14736381842, 38580227142, 101004149532, 264431978670
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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L. Euler, Observationes analyticae, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 54.
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LINKS
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FORMULA
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G.f.: 2*x*(1-2*x-x^2+x^3)/((1+x)*(1-3*x+x^2)*(1-x-x^2)).
a(n) = Fibonacci(n) + (1/5)*(Lucas(2*n) - 2*(-1)^n).
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PROG
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(PARI) a(n)=2*binomial(fibonacci(n)+1, 2)
(PARI) { for (n=0, 200, f=fibonacci(n); write("b059727.txt", n, " ", f*(f + 1)); ) } \\ Harry J. Smith, Jun 29 2009
(Magma) [ Fibonacci(n)*(Fibonacci(n)+1): n in [0..100]]; // Vincenzo Librandi, Apr 15 2011
(Haskell)
a059727 n = a059727_list !! n
a059727_list = zipWith (*) a000045_list $ map (+ 1) a000045_list
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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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STATUS
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approved
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