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A083879 a(0)=1, a(1)=4, a(n) = 8*a(n-1) - 14*a(n-2), n >= 2.

%I A083879 #18 Aug 25 2019 15:31:01
%S A083879 1,4,18,88,452,2384,12744,68576,370192,2001472,10829088,58612096,
%T A083879 317289536,1717746944,9299922048,50350919168,272608444672,
%U A083879 1475954689024,7991119286784,43265588647936,234249039168512,1268274072276992
%N A083879 a(0)=1, a(1)=4, a(n) = 8*a(n-1) - 14*a(n-2), n >= 2.
%C A083879 Binomial transform of A083878.
%C A083879 4th binomial transform of A077957. Inverse binomial transform of A083880. - _Philippe Deléham_, Nov 30 2008
%C A083879 From _L. Edson Jeffery_, Apr 26 2011: (Start)
%C A083879 Let G be the Gram matrix
%C A083879   G =
%C A083879   (4  1  0  1)
%C A083879   (1  4  1  0)
%C A083879   (0  1  4 -1)
%C A083879   (1  0 -1  4)
%C A083879 of A028997. Then a(n) = (1/4)*Trace(G^n). (End)
%H A083879 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-14).
%F A083879 a(n) = 2^((n-2)/2)*(2*sqrt(2)-1)^n + 2^((n-2)/2)*(2*sqrt(2)+1)^n;
%F A083879 a(n) = Sum_{k=0..n} C(n, 2k)*5^(n-2k)2^k.
%F A083879 G.f.: (1-4x)/(1-8x+14x^2).
%F A083879 E.g.f.: exp(4x)cosh(x*sqrt(2)).
%F A083879 ((4+sqrt(2))^n + (4-sqrt(2))^n)/2. Offset=0. a(3)=88. - Al Hakanson (hawkuu(AT)gmail.com), Oct 15 2008
%F A083879 a(n) = Sum_{k=0..n} A098158(n,k)*2^(3*k-n). - _Philippe Deléham_, Nov 30 2008
%t A083879 LinearRecurrence[{8,-14},{1,4},30] (* _Harvey P. Dale_, May 08 2013 *)
%Y A083879 Cf. A028997, A083880.
%K A083879 easy,nonn
%O A083879 0,2
%A A083879 _Paul Barry_, May 08 2003