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%I #26 Sep 08 2022 08:45:46
%S 5,3,15,9,45,27,135,81,405,243,1215,729,3645,2187,10935,6561,32805,
%T 19683,98415,59049,295245,177147,885735,531441,2657205,1594323,
%U 7971615,4782969,23914845,14348907,71744535,43046721,215233605,129140163,645700815,387420489
%N a(n) = 3*a(n-2) for n > 2; a(1) = 5, a(2) = 3.
%C Binomial transform is A162562.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F a(n) = (3-2*(-1)^n)*3^(1/4*(2*n-1+(-1)^n)).
%F G.f.: x*(5+3*x)/(1-3*x^2)
%t nxt[{a_,b_}]:={b,3a}; NestList[nxt,{5,3},40][[All,1]] (* or *) LinearRecurrence[ {0,3},{5,3},40] (* _Harvey P. Dale_, May 29 2021 *)
%o (Magma) [ n le 2 select 7-2*n else 3*Self(n-2): n in [1..34] ];
%Y Cf. A162562, A162436, A162766.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jul 20 2009
%E a(35)-a(36) from _Yifan Xie_, Jul 20 2022