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A343461
a(n) is the maximal number of congruent n-gons 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
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.
FORMULA
a(n) = floor(2*n/(n-2)).
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
Table[Floor[2 n/(n - 2)], {n, 3, 100}] (* Wesley Ivan Hurt, Apr 19 2021 *)
PROG
(PARI) a(n) = floor(n*(2/(n-2)))
(Magma) [Floor(2*n/(n-2)) : n in [3..100]]; // Wesley Ivan Hurt, Apr 19 2021
CROSSREFS
Cf. A071279.
Sequence in context: A217290 A157296 A329081 * A155044 A245634 A182618
KEYWORD
nonn,easy
AUTHOR
Felix Fröhlich, Apr 16 2021
STATUS
approved