This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164073 #36 Jun 30 2023 01:02:28
%S A164073 1,3,2,6,4,12,8,24,16,48,32,96,64,192,128,384,256,768,512,1536,1024,
%T A164073 3072,2048,6144,4096,12288,8192,24576,16384,49152,32768,98304,65536,
%U A164073 196608,131072,393216,262144,786432,524288,1572864,1048576,3145728,2097152,6291456
%N A164073 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
%C A164073 Interleaving of A000079 and A007283.
%C A164073 Binomial transform is A048654. Second binomial transform is A111567. Third binomial transform is A081179 without initial 0. Fourth binomial transform is A164072. Fifth binomial transform is A164031.
%C A164073 Absolute second differences are the sequence itself. - _Eric Angelini_, Jul 30 2013
%C A164073 Least number having n - 1 Gaussian prime factors, counted with multiplicity, excluding units. See A239628 for a similar sequence. - _T. D. Noe_, Mar 31 2014
%C A164073 Writing the prime factorizations of the terms of this sequence, the exponents of prime factor 2 give the integers repeated (A004526), while the exponents of prime factor 3 give the sequence of alternating 0's and 1's (A000035). - _Alonso del Arte_, Nov 30 2016
%H A164073 Vincenzo Librandi, <a href="/A164073/b164073.txt">Table of n, a(n) for n = 1..2000</a>
%H A164073 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2).
%F A164073 a(n) = (5 + (-1)^n) * 2^(1/4 * (2*n - 1 + (-1)^n))/4.
%F A164073 G.f.: x*(1 + 3 * x)/(1 - 2 * x^2).
%F A164073 a(n) = A074323(n), n>=1.
%F A164073 a(n) = A162255(n-1), n>=2.
%F A164073 a(n) = A072946(n-2), n > 2. - _R. J. Mathar_, Aug 17 2009
%F A164073 a(n+3) = a(n + 2) * a(n + 1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%F A164073 a(n) = (2/3)a(n - 1) for odd n > 1, a(n) = 3a(n - 1) for even n. - _Alonso del Arte_, Nov 30 2016
%t A164073 terms = 50; CoefficientList[Series[x * (1 + 3 * x)/(1 - 2 * x^2), {x, 0, terms}], x] (* _T. D. Noe_, Mar 31 2014 *)
%t A164073 Flatten[Table[{2^n, 3 * 2^n}, {n, 0, 31}]] (* _Alonso del Arte_, Nov 30 2016 *)
%t A164073 CoefficientList[Series[x (1 + 3 x)/(1 - 2 x^2), {x, 0, 44}], x] (* _Michael De Vlieger_, Dec 13 2016 *)
%o A164073 (Magma) [ n le 2 select 2*n-1 else 2*Self(n-2): n in [1..42] ];
%o A164073 (PARI) a(n) = (5 + (-1)^n) * 2^((2*n-9)\/4)
%o A164073 (PARI) Vec(x*(1+3*x)/(1-2*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A164073 Cf. A000079 (powers of 2), A007283 (3*2^n), A074323, A162255, A048654, A111567, A081179, A164072, A164031, A239628.
%K A164073 nonn,easy
%O A164073 1,2
%A A164073 _Klaus Brockhaus_, Aug 09 2009