http://forums.topcoder.com/;jsessionid=E9F9D7AD8268C70E91E2FBEC32D9EEBF?module=Thread&threadID=510405&start=0&mc=4#536735

For the first problem you can get an exact formula as an answer:

==> geometry/tiling/count.1x2.p <==
Count the ways to tile an MxN rectangle with 1x2 dominos.

==> geometry/tiling/count.1x2.s <==
The number of ways to tile an MxN rectangle with 1x2 dominos is
2^(M*N/2) times the product of

{ cos^2(m*pi/(M+1)) + cos^2(n*pi/(N+1)) } ^ (1/4)

over all m,n in the range 0<m><M+1, 0><n><N+1.

(this was taken from http://www.faqs.org/faqs/puzzles/archive/geometry/part1/ )

These problems are similar to the problem pavement which was a backup task in IOI 2001, you can find the solution here http://olympiads.win.tue.nl/ioi/ioi2001/contest/A-2001-7.pdf . 
Also the task bugs from ceoi 2002, you can find the problem and it's solution here: http://ics.upjs.sk/ceoi/Documents.html . 
Also this problem from topcoder ( http://www.topcoder.com/stat?c=problem_statement&pm=1706&rd=5855 ) is similar, you can find the solution here: http://www.topcoder.com/tc?module=Static&d1=match_editorials&d2=srm209 .>

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