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A059727 a(n) = Fibonacci(n)*(Fibonacci(n) + 1). 3
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)
OFFSET

0,2

REFERENCES

L. Euler, Observationes analyticae, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 54.

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, Séminaire Lotharingien de Combinatoire, B25f (1990), 1 p.

Eric Weisstein's World of Mathematics, Trinomial Coefficient

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).

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)); ) } \\ 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

-- Reinhard Zumkeller, Dec 17 2011

CROSSREFS

Sequence in context: A052994 A088219 A027375 * A103872 A216641 A191970

Adjacent sequences:  A059724 A059725 A059726 * A059728 A059729 A059730

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 09 2001

STATUS

approved

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Last modified May 24 23:11 EDT 2018. Contains 304538 sequences. (Running on oeis4.)