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A221173 a(0)=-3, a(1)=4; thereafter a(n) = 2*a(n-1) + a(n-2). 5

%I

%S -3,4,5,14,33,80,193,466,1125,2716,6557,15830,38217,92264,222745,

%T 537754,1298253,3134260,7566773,18267806,44102385,106472576,257047537,

%U 620567650,1498182837,3616933324,8732049485,21081032294,50894114073,122869260440,296632634953

%N a(0)=-3, a(1)=4; thereafter a(n) = 2*a(n-1) + a(n-2).

%H Reinhard Zumkeller, <a href="/A221173/b221173.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)*(7*sqrt(2)*((1+sqrt(2))^n-(1-sqrt(2))^n)-6*((1+sqrt(2))^n+(1-sqrt(2))^n)). - _Paolo P. Lava_, Jan 04 2013

%F a(n) = 10*A000129(n)-3*A000129(n+1). - _R. J. Mathar_, Jan 14 2013

%F G.f.: -(10*x-3) / (x^2+2*x-1). - _Colin Barker_, Jul 10 2015

%o (Haskell)

%o a221173 n = a221173_list !! n

%o a221173_list = -3 : 4 : zipWith (+)

%o (map (* 2) $ tail a221173_list) a221173_list

%o -- _Reinhard Zumkeller_, Jan 04 2013

%o (PARI) Vec(-(10*x-3)/(x^2+2*x-1) + O(x^100)) \\ _Colin Barker_, Jul 10 2015

%Y Cf. A000129, A078343, A221172, A221174, A221175.

%K sign,easy

%O 0,1

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

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Last modified August 15 01:28 EDT 2020. Contains 336484 sequences. (Running on oeis4.)