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A166481 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.

%I A166481 #13 Aug 02 2024 17:45:43
%S A166481 1,7,3,21,9,63,27,189,81,567,243,1701,729,5103,2187,15309,6561,45927,
%T A166481 19683,137781,59049,413343,177147,1240029,531441,3720087,1594323,
%U A166481 11160261,4782969,33480783,14348907,100442349,43046721,301327047
%N A166481 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.
%C A166481 Interleaving of A000244 and A005032.
%C A166481 Seventh binomial transform is A153598.
%H A166481 Vincenzo Librandi, <a href="/A166481/b166481.txt">Table of n, a(n) for n = 1..200</a>
%H A166481 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F A166481 a(n) = (5 + 2*(-1)^n)*3^((2*n - 5 + (-1)^n)/4).
%F A166481 G.f.: x*(1+7*x)/(1-3*x^2).
%F A166481 E.g.f.: (1/3)*(-7 + 7*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - _G. C. Greubel_, Aug 02 2024
%t A166481 LinearRecurrence[{0,3},{1,7},50] (* or *) Flatten[NestList[3#&,{1,7},20]] (* _Harvey P. Dale_, Sep 24 2015 *)
%o A166481 (Magma) [ n le 2 select 6*n-5 else 3*Self(n-2): n in [1..34] ];
%o A166481 (SageMath)
%o A166481 def A166481(n): return 3^(n/2)*(sqrt(3)*(n%2) + 7*((n+1)%2))/3
%o A166481 [A166481(n) for n in range(1,41)] # _G. C. Greubel_, Aug 02 2024
%Y A166481 Cf. A000244 (powers of 3), A005032 (7*3^n), A153598.
%K A166481 nonn
%O A166481 1,2
%A A166481 _Klaus Brockhaus_, Oct 14 2009