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A166552 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.

%I A166552 #19 Sep 08 2022 08:45:48
%S A166552 1,4,3,12,9,36,27,108,81,324,243,972,729,2916,2187,8748,6561,26244,
%T A166552 19683,78732,59049,236196,177147,708588,531441,2125764,1594323,
%U A166552 6377292,4782969,19131876,14348907,57395628,43046721,172186884,129140163
%N A166552 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.
%C A166552 Interleaving of A000244 (powers of 3) and 4*A000244.
%C A166552 a(n) = A074324(n); A074324 has the additional term a(0)=1.
%C A166552 First differences are in A162852.
%C A166552 Second binomial transform is A054491. Fourth binomial transform is A153594.
%H A166552 G. C. Greubel, <a href="/A166552/b166552.txt">Table of n, a(n) for n = 1..1000</a>[Terms 1 through 300 were computed by Vincenzo Librandi; Terms 301 through 1000 by G. C. Greubel, May 17 2016]
%H A166552 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3)
%F A166552 a(n) = (7+(-1)^n)*3^(1/4*(2*n-5+(-1)^n))/2.
%F A166552 G.f.: x*(1+4*x)/(1-3*x^2).
%F A166552 a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%F A166552 a(n) = 3^floor((n-1)/2)*4^(1-n%2). - _M. F. Hasler_, Dec 03 2014
%F A166552 E.g.f.: (sqrt(3)*sinh(sqrt(3)*x) + 4*cosh(sqrt(3)*x) - 4)/3. - _Ilya Gutkovskiy_, May 17 2016
%t A166552 LinearRecurrence[{0, 3}, {1, 4}, 50] (* _G. C. Greubel_, May 17 2016 *)
%o A166552 (Magma) [ n le 2 select 3*n-2 else 3*Self(n-2): n in [1..35] ];
%o A166552 (PARI) a(n)=3^(n\2)*(4/3)^!bittest(n,0) \\ _M. F. Hasler_, Dec 03 2014
%Y A166552 Equals A162766 preceded by 1.
%Y A166552 Cf. A000244 (powers of 3), A074324, A162852, A054491, A153594.
%K A166552 nonn
%O A166552 1,2
%A A166552 _Klaus Brockhaus_, Oct 16 2009