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

1,1

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).

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

Mathematica

LinearRecurrence[{0, 2}, {3, 4, 6, 8}, 52]] (* or *) Table[(1/2)*(5-(-1)^n )*2^((2*n-1+(-1)^n)/4), {n, 50}] (* G. C. Greubel, Aug 24 2017 *)

Prog

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

Crossrefs

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

Sequence in context: A299252 A299253 A063759 * A145751 A277099 A146566

Adjacent sequences: A163975 A163976 A163977 * A163979 A163980 A163981

Keyword

nonn,easy

Author

Klaus Brockhaus, Aug 07 2009

Status

approved