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 A163978 #34 Jun 10 2025 23:16:10
%S A163978 3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1024,1536,2048,
%T A163978 3072,4096,6144,8192,12288,16384,24576,32768,49152,65536,98304,131072,
%U A163978 196608,262144,393216,524288,786432,1048576,1572864,2097152,3145728
%N A163978 a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4.
%C A163978 Interleaving of A007283 and A000079 without initial terms 1 and 2.
%C A163978 Equals A029744 without first two terms. Agrees with A145751 for all terms listed there (up to 65536).
%C A163978 Binomial transform is A078057 without initial 1, second binomial transform is A048580, third binomial transform is A163606, fourth binomial transform is A163604, fifth binomial transform is A163605.
%C A163978 a(n) is the number of vertices of the (n-1)-iterated line digraph L^{n-1}(G) of the digraph G(=L^0(G)) with vertices u,v,w and arcs u->v, v->u, v->w, w->v. - _Miquel A. Fiol_, Jun 08 2024
%H A163978 Vincenzo Librandi, <a href="/A163978/b163978.txt">Table of n, a(n) for n = 1..2000</a>
%H A163978 Miquel A. Fiol, J. L. A. Yebra, and I. Alegre, <a href="https://doi.org/10.1109/TC.1984.1676455">Line digraph iterations and the (d,k) digraph problem</a>, IEEE Trans. Comput. C-33(5) (1984), 400-403.
%H A163978 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A163978 a(n) = A027383(n-1) + 2.
%F A163978 a(n) = A052955(n) + 1 for n >= 1.
%F A163978 a(n) = (1/2)*(5 - (-1)^n)*2^((2*n - 1 + (-1)^n)/4).
%F A163978 G.f.: x*(3+4*x)/(1-2*x^2).
%F A163978 a(n) = A090989(n-1).
%F A163978 E.g.f.: (1/2)*(4*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) - 4). - _G. C. Greubel_, Aug 24 2017
%F A163978 a(n) = A063759(n), n >= 1. - _R. J. Mathar_, Jan 25 2023
%t A163978 LinearRecurrence[{0,2}, {3,4}, 52] (* or *) Table[(1/2)*(5-(-1)^n )*2^((2*n-1+(-1)^n)/4), {n,50}] (* _G. C. Greubel_, Aug 24 2017 *)
%o A163978 (Magma) [ n le 2 select n+2 else 2*Self(n-2): n in [1..41] ];
%o A163978 (PARI) my(x='x+O('x^50)); Vec(x*(3+4*x)/(1-2*x^2)) \\ _G. C. Greubel_, Aug 24 2017
%o A163978 (SageMath) [(2+(n%2))*2^((n-(n%2))//2) for n in range(1,41)] # _G. C. Greubel_, Jun 13 2024
%Y A163978 Cf. A000079 (powers of 2), A007283 (3*2^n), A027383, A029744, A048580, A052955, A063759, A078057, A090989, A145751, A163604, A163605, A163606.
%K A163978 nonn,easy
%O A163978 1,1
%A A163978 _Klaus Brockhaus_, Aug 07 2009