A221172 a(0)=-2, a(1)=3; thereafter a(n) = 2*a(n-1) + a(n-2).

-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

Offset

0,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (2,1).

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

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

Cf. A000129, A078343, A221173, A221174, A221175.

Sequence in context: A357360 A301877 A369438 * A116054 A339782 A176621

Adjacent sequences: A221169 A221170 A221171 * A221173 A221174 A221175

Keyword

sign,easy

Author

N. J. A. Sloane, Jan 04 2013

Status

approved