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A080879 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=6.

%I A080879 #25 Jun 12 2024 10:33:44
%S A080879 1,1,6,7,44,52,328,388,2448,2896,18272,21616,136384,161344,1017984,
%T A080879 1204288,7598336,8988928,56714752,67094272,423324672,500798464,
%U A080879 3159738368,3738010624,23584608256,27900891136,176037912576,208255086592,1313964867584,1554437128192
%N A080879 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=6.
%H A080879 Harvey P. Dale, <a href="/A080879/b080879.txt">Table of n, a(n) for n = 0..1000</a>
%H A080879 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-4).
%F A080879 a(2n) = A080876(2n+3)/2, a(2n+1) = A080876(2n+4)/4.
%F A080879 G.f.: (-x^3 - 2*x^2 + x + 1)/(4*x^4 - 8*x^2 + 1).
%F A080879 a(n) = ((9/16)*sqrt(3) - 7/16)*(1 + sqrt(3))^n + (-(9/16)*sqrt(3) - 7/16)*(1 - sqrt(3))^n + (-(19/48)*sqrt(3) + 15/16)*(-(1 + sqrt(3)))^n + ((19/48)*sqrt(3) + 15/16)*(-(1 - sqrt(3)))^n. - _Richard Choulet_, Dec 06 2008
%F A080879 a(n+4) = 8*a(n+2) - 4*a(n). - _Richard Choulet_, Dec 06 2008
%p A080879 a:= n-> (<<0|1>, <-4|8>>^floor(n/2). <<1, 6+(n mod 2)>>)[1,1]:
%p A080879 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 18 2023
%t A080879 LinearRecurrence[{0,8,0,-4},{1,1,6,7},30] (* _Harvey P. Dale_, Mar 10 2015 *)
%Y A080879 Cf. A080876, A080877, A080878, A080880, A080881, A080882.
%K A080879 nonn
%O A080879 0,3
%A A080879 _Paul D. Hanna_, Feb 22 2003