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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 09 2001
STATUS
approved