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A267652 a(n) = 4*a(n - 1) + 4*a(n - 2) for n>1, a(0)=2, a(1)=3.

%I A267652 #15 Jun 07 2016 13:05:14
%S A267652 2,3,20,92,448,2160,10432,50368,243200,1174272,5669888,27376640,
%T A267652 132186112,638251008,3081748480,14879997952,71846985728,346907934720,
%U A267652 1675019681792,8087710466048,39050920591360,188554524229632,910421779283968,4395905214054400,21225307973353472,102484852749631488
%N A267652 a(n) = 4*a(n - 1) + 4*a(n - 2) for n>1, a(0)=2, a(1)=3.
%C A267652 Generalized Fibonacci sequence.
%H A267652 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,4).
%F A267652 G.f.: (2 - 5*x)/(1 - 4*x - 4*x^2).
%F A267652 a(n) = 2^(n-5/2)*((1+4*sqrt(2))*(1-sqrt(2))^n - (1-4*sqrt(2))*(1+sqrt(2))^n).
%F A267652 Lim_{n -> infinity} a(n)/a(n - 1) = 2 + 2*sqrt(2) = 2*A014176 = 4.82842712...
%F A267652 a(n) = 2*A057087(n)-5*A057087(n-1). - _R. J. Mathar_, Jun 07 2016
%t A267652 Table[2^(n - 5/2) ((1 + 4 Sqrt[2]) (1 - Sqrt[2])^n - (1 - 4 Sqrt[2]) (1 + Sqrt[2])^n), {n, 0, 25}]
%t A267652 RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == 4 a[n - 1] + 4 a[n - 2]}, a, {n, 25}] (* _Bruno Berselli_, Jan 19 2016 *)
%t A267652 LinearRecurrence[{4, 4}, {2, 3}, 20] (* _Vincenzo Librandi_, Jan 19 2016 *)
%o A267652 (PARI) Vec((2-5*x)/(1-4*x-4*x^2) + O(x^100)) \\ _Altug Alkan_, Jan 19 2016
%Y A267652 Cf. A057087, A084128.
%K A267652 nonn,easy
%O A267652 0,1
%A A267652 _Ilya Gutkovskiy_, Jan 19 2016