A185634 Number of n-length cycles from any point in a complete graph on n nodes.

1, 2, 21, 204, 2605, 39990, 720601, 14913080, 348678441, 9090909090, 261535698061, 8230246567620, 281241170407093, 10371206370520814, 410525522232055665, 17361641481138401520, 781282469559318055057, 37275544492386193492506, 1879498672877297909667781

Offset: 2

Author

Sébastien Dumortier, Dec 18 2012

Keywords

• easy
• nonn

Comments

If M is the n X n matrix filled with ones, a(n) is the upper left element of (M-Id)^n.

Examples

			In a complete graph in 5 nodes, there are 204 different cycles with a length of 5, from a point to itself.
		

Crossrefs

Cf. A173499.

Formula

a(n) = floor((n-1)^n/n) + ((-1)^n+1)/2.

a(n) = floor((n-1)^n/n)+1 for n odd, a(n) = floor((n-1)^n/n) for n even.