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A221172
a(0)=-2, a(1)=3; thereafter a(n) = 2*a(n-1) + a(n-2).
5
-2, 3, 4, 11, 26, 63, 152, 367, 886, 2139, 5164, 12467, 30098, 72663, 175424, 423511, 1022446, 2468403, 5959252, 14386907, 34733066, 83853039, 202439144, 488731327, 1179901798, 2848534923, 6876971644, 16602478211, 40081928066, 96766334343, 233614596752, 563995527847
OFFSET
0,1
LINKS
José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368 [cs.DM], 2012-2014.
FORMULA
G.f.: (2-7*x)/(-1+2*x+x^2). - R. J. Mathar, Jan 04 2013
a(n) = 7*Pell(n) - 2*Pell(n+1), where Pell = A000129. - Vladimir Reshetnikov, Sep 27 2016
E.g.f.: -2*exp(x)*cosh(sqrt(2)*x) + 5*exp(x)*sinh(sqrt(2)*x)/sqrt(2). - Stefano Spezia, May 26 2024
MATHEMATICA
LinearRecurrence[{2, 1}, {-2, 3}, 40] (* Harvey P. Dale, May 30 2013 *)
Table[7 Fibonacci[n, 2] - 2 Fibonacci[n + 1, 2], {n, 0, 30}] (* Vladimir Reshetnikov, Sep 27 2016 *)
PROG
(Haskell)
a221172 n = a221172_list !! n
a221172_list = -2 : 3 : zipWith (+)
(map (* 2) $ tail a221172_list) a221172_list
-- Reinhard Zumkeller, Jan 04 2013
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Jan 04 2013
STATUS
approved