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A185634 Number of n-length cycles from any point in a complete graph on n nodes. 1

%I #14 Dec 31 2012 10:05:59

%S 1,2,21,204,2605,39990,720601,14913080,348678441,9090909090,

%T 261535698061,8230246567620,281241170407093,10371206370520814,

%U 410525522232055665,17361641481138401520,781282469559318055057,37275544492386193492506,1879498672877297909667781

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

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

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

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

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

%Y Cf. A173499.

%K easy,nonn

%O 2,2

%A _S├ębastien Dumortier_, Dec 18 2012

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Last modified February 25 00:12 EST 2024. Contains 370308 sequences. (Running on oeis4.)