A206601 3^(n(n+1)/2) - 1.

0, 2, 26, 728, 59048, 14348906, 10460353202, 22876792454960, 150094635296999120, 2954312706550833698642, 174449211009120179071170506, 30903154382632612361920641803528, 16423203268260658146231467800709255288, 26183890704263137277674192438430182020124346

Offset: 0

Author

Ivan N. Ianakiev, Feb 10 2012

Keywords

• easy
• nonn

Comments

There are n cities located on the vertices of a convex n-gon and 2 types of communication lines available. Any city can be connected to any other by only one communication line (that can be of any type). A network exists if at least 2 cities are connected by a communication line. The sequence shows how many different networks a(n) can be built. In general, if the number of communication-line types is c, then a(n) = (c+1)^(n(n+1)/2)-1. Thus other sequences of this type can be generated.

Examples

			In the case of 2 different types of communication lines and 4 cities, the number of different networks (connecting at least 2 cities) is 728.
		

Crossrefs

Cf. A000217, A126883.

Formula

a(n) = (3^A000217) - 1.

a(n) = A047656(n+1) - 1. - Omar E. Pol, Feb 18 2012