Guy's Conjecture

Author

Eric W. Weisstein
May 3, 2019

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/GuysConjecture.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GuysConjecture.html.

©2019 Wolfram Research, Inc. except for portions noted otherwise

Compute

Guy[n_]:=(1/4)Floor[(n/2)]Floor[((n-1)/2)]Floor[((n-2)/2)]Floor[((n-3)/2)]

Guy/@Range[12]

FullSimplify[Guy[n],n∈Integers&&n>0]

FullSimplify[Guy[n],n∈Integers&&n>0&&Mod[n,1]==0]

Table[{Guy[n],(n-1)^2(n-3)^2/64},{n,1,15,2}]

FullSimplify[Guy[n],n∈Integers&&n>0&&Mod[n,2]==0]

Table[{Guy[n],n(n-2)^2(n-4)/64},{n,2,10,2}]