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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 (list; graph; refs; listen; history; text; internal format)
 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 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 Adjacent sequences: A343458 A343459 A343460 * A343462 A343463 A343464 KEYWORD nonn,easy AUTHOR Felix Fröhlich, Apr 16 2021 STATUS approved

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Last modified August 9 16:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)