Unique Paths on a 3 x 7 grid (right and down only)
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           0   1   2   3   4   5   6
row 0      1   1   1   1   1   1   1
row 1      1   2   3   4   5   6   7
row 2      1   3   6  10  15  21  28

answer = bottom-right cell = 28
10 x 10 grid: table = 48620, one row = 48620, binomial C(18,9) = 48620