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

%I #19 Sep 08 2022 08:45:48

%S 1,4,3,12,9,36,27,108,81,324,243,972,729,2916,2187,8748,6561,26244,

%T 19683,78732,59049,236196,177147,708588,531441,2125764,1594323,

%U 6377292,4782969,19131876,14348907,57395628,43046721,172186884,129140163

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

%C Interleaving of A000244 (powers of 3) and 4*A000244.

%C a(n) = A074324(n); A074324 has the additional term a(0)=1.

%C First differences are in A162852.

%C Second binomial transform is A054491. Fourth binomial transform is A153594.

%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3)

%F a(n) = (7+(-1)^n)*3^(1/4*(2*n-5+(-1)^n))/2.

%F G.f.: x*(1+4*x)/(1-3*x^2).

%F a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011

%F a(n) = 3^floor((n-1)/2)*4^(1-n%2). - _M. F. Hasler_, Dec 03 2014

%F E.g.f.: (sqrt(3)*sinh(sqrt(3)*x) + 4*cosh(sqrt(3)*x) - 4)/3. - _Ilya Gutkovskiy_, May 17 2016

%t LinearRecurrence[{0, 3}, {1, 4}, 50] (* _G. C. Greubel_, May 17 2016 *)

%o (Magma) [ n le 2 select 3*n-2 else 3*Self(n-2): n in [1..35] ];

%o (PARI) a(n)=3^(n\2)*(4/3)^!bittest(n,0) \\ _M. F. Hasler_, Dec 03 2014

%Y Equals A162766 preceded by 1.

%Y Cf. A000244 (powers of 3), A074324, A162852, A054491, A153594.

%K nonn

%O 1,2

%A _Klaus Brockhaus_, Oct 16 2009