Rectangle Tiling

Author

Eric W. Weisstein
December 17, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Tilings/RectangleTiling.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Sums

(∑_(j=0)^(n-1))(∑_(i=0)^(m-1))(m-i) (n-j)==(1/4) m (m+1) n (n+1)

Sum[(m-i)(n-j),{j,0,n-1},{i,0,m-1}]

(Binomial[m+1, 2]) (Binomial[n+1, 2])==(1/4) m (m+1) n (n+1)

Binomial[m+1,2]Binomial[n+1,2]