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A221172 a(0)=-2, a(1)=3; thereafter a(n) = 2*a(n-1) + a(n-2). 5

%I

%S -2,3,4,11,26,63,152,367,886,2139,5164,12467,30098,72663,175424,

%T 423511,1022446,2468403,5959252,14386907,34733066,83853039,202439144,

%U 488731327,1179901798,2848534923,6876971644,16602478211,40081928066,96766334343,233614596752

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

%H Reinhard Zumkeller, <a href="/A221172/b221172.txt">Table of n, a(n) for n = 0..1000</a>

%H José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, <a href="http://arxiv.org/abs/1212.1368">A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake</a>, arXiv preprint arXiv:1212.1368, 2012

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).

%F 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]

%F G.f. ( 2-7*x ) / ( -1+2*x+x^2 ). - _R. J. Mathar_, Jan 04 2013

%F a(n) = 7*Pell(n) - 2*Pell(n+1), where Pell = A000129. - _Vladimir Reshetnikov_, Sep 27 2016

%t LinearRecurrence[{2,1},{-2,3},40] (* _Harvey P. Dale_, May 30 2013 *)

%t Table[7 Fibonacci[n, 2] - 2 Fibonacci[n + 1, 2], {n, 0, 30}] (* _Vladimir Reshetnikov_, Sep 27 2016 *)

%o (Haskell)

%o a221172 n = a221172_list !! n

%o a221172_list = -2 : 3 : zipWith (+)

%o (map (* 2) $ tail a221172_list) a221172_list

%o -- _Reinhard Zumkeller_, Jan 04 2013

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

%K sign,easy

%O 0,1

%A _N. J. A. Sloane_, Jan 04 2013

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)