A lattice path from one point to another is p-good if it lies completely below the line y = (p - 1) x. Hilton and Pederson show that the number of p-good paths from (1, q - 1) to (k, n - k) under the condition 2<=k<=n - p + 1<=p(k - 1) is (n - q k - 1) - sum_(j = 1)^ℓ _p d_(q j)(n - p j k - j), where (a b) is a binomial coefficient, and ℓ congruent ⌊(n - k)/(p - 1) ⌋, where ⌊x⌋ is the floor function.
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