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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 (list; graph; refs; listen; history; text; internal format)
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, 2012

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

FORMULA

a(n)=(1/4)*(5*sqrt(2)*((1+sqrt(2))^n-(1-sqrt(2))^n)-4*((1+sqrt(2))^n+(1-sqrt(2))^n)). [Paolo P. Lava, Jan 04 2013]

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: A037396 A037432 A301877 * A116054 A176621 A099527

Adjacent sequences:  A221169 A221170 A221171 * A221173 A221174 A221175

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Jan 04 2013

STATUS

approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)