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4. (romanian national olympiad, 10th grade 2000) How many ways can you tile a 3xn rectangle with dominoes.
5.
[code]
for i1 = 1 to n
for i2 = i1 to n
for i3 = i2 to n
for i[1] = 1 to n
for i[2] = i[1] to n
for i[3] = i[2] to n
…
for ik = ik - 1 to n
for i[k] = i[k - 1] to n
print ‘*’
[/code]
How many stars will be printed for a given n and k.
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