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A278705 Number of length-4 cycles in all simple labeled graphs on n nodes. 1
12, 960, 92160, 13762560, 3523215360, 1623497637888, 1385384650997760, 2229281815548395520, 6848353737364671037440, 40517904423021555933511680, 464691742246749620690258755584, 10382058415869198798257999252029440, 453599053561602541628424159320667586560 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Table of n, a(n) for n=4..16.

Peter Maceli, Class Nine: Random Graphs

FORMULA

a(n) = binomial(n,4)*(4!/8)*2^binomial(n,2). The number of length k cycles in all simple labeled graphs on n nodes is binomial(n,k)*(k!/(2*k))*2^binomial(n,2).

MATHEMATICA

Table[FactorialPower[n, 4]/(8) 2^(Binomial[n, 2] - 4), {n, 0, 15}]

PROG

(MAGMA) [n*(n-1)*(n-2)*(n-3)/8*2^(Binomial(n, 2)-4): n in [4..20]]; // _Vincenzo Lubrandi_, Nov 27 2016

CROSSREFS

Sequence in context: A114809 A114371 A047802 * A180237 A079916 A204327

Adjacent sequences:  A278702 A278703 A278704 * A278706 A278707 A278708

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Nov 26 2016

STATUS

approved

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Last modified April 5 03:15 EDT 2020. Contains 333238 sequences. (Running on oeis4.)