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Search: id:A059727
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| A059727 |
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Fibonacci(n)*(Fibonacci(n)+1). |
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+0
2
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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; listen)
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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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Harry J. Smith, Table of n, a(n) for n=0,...,200
G. E. Andrews, Three aspects of partitions
Eric Weisstein's World of Mathematics, Trinomial Coefficient
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FORMULA
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G.f.: 2x(1-2x-x^2+x^3)/((1+x)(1-3x+x^2)(1-x-x^2)).
Fib(n) + (1/5)[Lucas(2n) - 2(-1)^n].
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PROGRAM
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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)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 29 2009]
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CROSSREFS
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Sequence in context: A052994 A088219 A027375 this_sequence A103872 A159322 A049313
Adjacent sequences: A059724 A059725 A059726 this_sequence A059728 A059729 A059730
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 09 2001
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