A163978 a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4.

3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152, 3145728

Offset: 1

Author

Klaus Brockhaus, Aug 07 2009

Keywords

• nonn
• easy

Comments

Interleaving of A007283 and A000079 without initial terms 1 and 2.

Equals A029744 without first two terms. Agrees with A145751 for all terms listed there (up to 65536).

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.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Miquel A. Fiol, J. L. A. Yebra, and I. Alegre, Line digraph iterations and the (d,k) digraph problem, IEEE Trans. Comput. C-33(5) (1984), 400-403.
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A000079 (powers of 2), A007283 (3*2^n), A027383, A029744, A048580, A052955, A063759, A078057, A090989, A145751, A163604, A163605, A163606.

Programs

Magma

[ n le 2 select n+2 else 2*Self(n-2): n in [1..41] ];

Mathematica

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 *)

PARI

my(x='x+O('x^50)); Vec(x*(3+4*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 24 2017

SageMath

[(2+(n%2))*2^((n-(n%2))//2) for n in range(1,41)] # G. C. Greubel, Jun 13 2024

Formula

a(n) = A027383(n-1) + 2.

a(n) = A052955(n) + 1 for n >= 1.

a(n) = (1/2)*(5 - (-1)^n)*2^((2*n - 1 + (-1)^n)/4).

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

a(n) = A090989(n-1).

E.g.f.: (1/2)*(4*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) - 4). - G. C. Greubel, Aug 24 2017

a(n) = A063759(n), n >= 1. - R. J. Mathar, Jan 25 2023