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

%I A221172 #31 May 26 2024 08:22:34
%S A221172 -2,3,4,11,26,63,152,367,886,2139,5164,12467,30098,72663,175424,
%T A221172 423511,1022446,2468403,5959252,14386907,34733066,83853039,202439144,
%U A221172 488731327,1179901798,2848534923,6876971644,16602478211,40081928066,96766334343,233614596752,563995527847
%N A221172 a(0)=-2, a(1)=3; thereafter a(n) = 2*a(n-1) + a(n-2).
%H A221172 Reinhard Zumkeller, <a href="/A221172/b221172.txt">Table of n, a(n) for n = 0..1000</a>
%H A221172 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 [cs.DM], 2012-2014.
%H A221172 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%F A221172 G.f.: (2-7*x)/(-1+2*x+x^2). - _R. J. Mathar_, Jan 04 2013
%F A221172 a(n) = 7*Pell(n) - 2*Pell(n+1), where Pell = A000129. - _Vladimir Reshetnikov_, Sep 27 2016
%F A221172 E.g.f.: -2*exp(x)*cosh(sqrt(2)*x) + 5*exp(x)*sinh(sqrt(2)*x)/sqrt(2). - _Stefano Spezia_, May 26 2024
%t A221172 LinearRecurrence[{2,1},{-2,3},40] (* _Harvey P. Dale_, May 30 2013 *)
%t A221172 Table[7 Fibonacci[n, 2] - 2 Fibonacci[n + 1, 2], {n, 0, 30}] (* _Vladimir Reshetnikov_, Sep 27 2016 *)
%o A221172 (Haskell)
%o A221172 a221172 n = a221172_list !! n
%o A221172 a221172_list = -2 : 3 : zipWith (+)
%o A221172                         (map (* 2) $ tail a221172_list) a221172_list
%o A221172 -- _Reinhard Zumkeller_, Jan 04 2013
%Y A221172 Cf. A000129, A078343, A221173, A221174, A221175.
%K A221172 sign,easy
%O A221172 0,1
%A A221172 _N. J. A. Sloane_, Jan 04 2013