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%I #25 Mar 02 2023 13:42:00
%S 1,3,12,57,291,1524,8049,42627,225948,1197993,6352419,33684996,
%T 178623201,947197443,5022773292,26634636057,141237492771,748950724884,
%U 3971517639249,21060066950787,111676809902268,592197066758793
%N a(0)=1, a(1)=3, a(n) = 7*a(n-1) - 9*a(n-2) for n > 1.
%C a(n)/a(n-1) tends to (7+sqrt(13))/2 = 5.30277563... = 2+A098316.
%C For n >= 2, a(n) equals 3^n times the permanent of the (2n-2) X (2n-2) matrix with 1/sqrt(3)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. - _John M. Campbell_, Jul 08 2011
%H Vincenzo Librandi, <a href="/A165310/b165310.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-9).
%F G.f.: (1-4x)/(1-7x+9x^2).
%F a(n) = Sum_{k=0..n} A165253(n,k)*3^(n-k).
%F a(n) = ((13-sqrt(13))*(7+sqrt(13))^n+(13+sqrt(13))*(7-sqrt(13))^n )/(26*2^n). - _Klaus Brockhaus_, Sep 26 2009
%t LinearRecurrence[{7,-9},{1,3},30] (* _Harvey P. Dale_, Sep 23 2011 *)
%o (Magma) I:=[1,3]; [n le 2 select I[n] else 7*Self(n-1)-9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Sep 24 2011
%Y Cf. A098316, A165253.
%K nonn
%O 0,2
%A _Philippe Deléham_, Sep 14 2009
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