

A343461


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


1



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 ngon tends towards 180 degrees, so a(n) = 2 for n > 6.
This also shows that no regular ngon can tile the plane for n > 6 since in any tiling by convex tiles at least three tiles meet at every vertex.


LINKS



FORMULA

a(n) = floor(2*n/(n2)).


EXAMPLE

For n = 5: Arranging 3 pentagons around a vertex leaves a gap smaller than the internal angle of a pentagon, so a(5) = 3.


MATHEMATICA



PROG

(PARI) a(n) = floor(n*(2/(n2)))


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



