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Formulas for the number of gridlines. (English) Zbl 1250.05023
Summary: Let $$l(n)$$ be the number of lines through at least two points of an $$n \times n$$ rectangular grid. We prove recursive and asymptotic formulas for it using respectively combinatorial and number theoretic methods. We also study the ratio $$l(n)/l(n-1)$$. All this originates from Mustonen’s experimental results [Seppo Mustonen, “On lines and their intersection points in a rectangular grid of points,” http://www.survo.fi/papers/PointsInGrid.pdf].

MSC:
 05A19 Combinatorial identities, bijective combinatorics 11B37 Recurrences 11N37 Asymptotic results on arithmetic functions 11P21 Lattice points in specified regions
OEIS
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References:
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