A343461 - OEIS

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A343461

a(n) is the maximal number of congruent n-gons that can be arranged around a vertex without overlapping.

6, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

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OFFSET

3,1

COMMENTS

As n increases, the internal angle of the n-gon tends towards 180 degrees, so a(n) = 2 for n > 6.

This also shows that no regular n-gon can tile the plane for n > 6 since in any tiling by convex tiles at least three tiles meet at every vertex.

LINKS

Table of n, a(n) for n=3..89.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

a(n) = floor(2*n/(n-2)).

EXAMPLE