A343461 a(n) is the maximal number of regular 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

Offset: 3

Author

Felix Fröhlich, Apr 16 2021

Keywords

• nonn
• easy

Comments

As n increases, the internal angle of the regular 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.

Examples

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

Links

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

Crossrefs

Cf. A071279.

Programs

Magma

[Floor(2*n/(n-2)) : n in [3..100]]; // Wesley Ivan Hurt, Apr 19 2021

Mathematica

Table[Floor[2 n/(n - 2)], {n, 3, 100}] (* Wesley Ivan Hurt, Apr 19 2021 *)

PARI

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

Formula

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

Extensions

Edited by Peter Munn, Mar 18 2025