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A166465 a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 5.

%I A166465 #12 Jul 27 2024 03:17:24
%S A166465 1,5,3,15,9,45,27,135,81,405,243,1215,729,3645,2187,10935,6561,32805,
%T A166465 19683,98415,59049,295245,177147,885735,531441,2657205,1594323,
%U A166465 7971615,4782969,23914845,14348907,71744535,43046721,215233605,129140163
%N A166465 a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
%C A166465 Interleaving of A000244 and A005030.
%C A166465 Second binomial transform is A054485.
%C A166465 Fifth binomial transform is A153596.
%H A166465 Vincenzo Librandi, <a href="/A166465/b166465.txt">Table of n, a(n) for n = 1..1000</a>
%H A166465 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F A166465 a(n) = (4 + (-1)^n) * 3^((2*n - 5 + (-1)^n)/4).
%F A166465 G.f.: x*(1+5*x)/(1-3*x^2).
%F A166465 a(n) = A162813(n-1), for n >= 2.
%F A166465 From _G. C. Greubel_, Jul 27 2024: (Start)
%F A166465 a(n) = (1/6)*3^(n/2)*( 5*(1+(-1)^n) + sqrt(3)*(1-(-1)^n) ).
%F A166465 E.g.f.: (1/3)*(sqrt(3)*sinh(sqrt(3)*x) + 10*(sinh(sqrt(3)*x/2))^2). (End)
%t A166465 LinearRecurrence[{0,3}, {1,5}, 41] (* _G. C. Greubel_, Jul 27 2024 *)
%o A166465 (Magma) [ n le 2 select 4*n-3 else 3*Self(n-2): n in [1..35] ];
%o A166465 (SageMath) [3^(n/2)*(5*((n+1)%2) +sqrt(3)*(n%2))/3 for n in range(1,41)] # _G. C. Greubel_, Jul 27 2024
%Y A166465 Cf. A000244 (powers of 3), A005030 (5*3^n), A054485, A153596, A162813.
%K A166465 nonn,easy
%O A166465 1,2
%A A166465 _Klaus Brockhaus_, Oct 14 2009