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A059727
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Fibonacci(n)*(Fibonacci(n)+1).
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3
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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; internal format)
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OFFSET
| 0,2
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REFERENCES
| L. Euler, Observationes analyticae, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 54.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..300 [replacing table for n = 0..200 by Harry J. Smith]
G. E. Andrews, Three aspects of partitions
Eric Weisstein's World of Mathematics, Trinomial Coefficient
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FORMULA
| 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
| (PARI) a(n)=2*binomial(fibonacci(n)+1, 2)
(PARI) { for (n=0, 200, f=fibonacci(n); write("b059727.txt", n, " ", f*(f + 1)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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
-- Reinhard Zumkeller, Dec 17 2011
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CROSSREFS
| Sequence in context: A052994 A088219 A027375 * A103872 A191970 A175516
Adjacent sequences: A059724 A059725 A059726 * A059728 A059729 A059730
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 09 2001
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