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%I #20 Jan 28 2023 12:01:35
%S 6,10,12,14,16,18,18,20,22,22,24,24,26,26,28,28,30,30,30,32,32,34,34,
%T 34,36,36,36,38,38,38,40,40,40,42,42,42,42,44,44,44,46,46,46,46,48,48,
%U 48,48,50,50,50,50,52,52,52,52,54,54,54,54,54,56,56,56,56,58,58,58,58,58,60,60
%N Minimal perimeter of a polyhex with n cells.
%D Y. S. Kupitz, "On the maximal number of appearances of the minimal distance among n points in the plane", in Intuitive geometry: Proceedings of the 3rd international conference held in Szeged, Hungary, 1991; Amsterdam: North-Holland: Colloq. Math. Soc. Janos Bolyai. 63, 217-244.
%H Michael De Vlieger, <a href="/A135711/b135711.txt">Table of n, a(n) for n = 1..10000</a>
%H Li Gan, Stéphane Ouvry, and Alexios P. Polychronakos, <a href="https://arxiv.org/abs/2107.10851">Algebraic area enumeration of random walks on the honeycomb lattice</a>, arXiv:2107.10851 [math-ph], 2021.
%H Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, <a href="https://doi.org/10.1007/s00026-022-00631-1">Extremal {p, q}-Animals</a>, Ann. Comb. (2023). See Corollary 1.9 at p. 8.
%F It is easy to use the formula of Harborth given in A135708 to show that a(n) = 2*ceiling(sqrt(12*n-3)). - _Sascha Kurz_, Mar 05 2008
%F 2*A135708(n) - a(n) = 6n. - _Tanya Khovanova_, Mar 07 2008
%t Table[2Ceiling[Sqrt[12n-3]],{n,120}] (* _Harvey P. Dale_, Dec 29 2019 *)
%Y Cf. A000228 (number of hexagonal polyominoes (or planar polyhexes) with n cells), A135708.
%Y Analogs for triangles, squares, cubes: A067628, A027709, A075777.
%K nonn
%O 1,1
%A _Tanya Khovanova_, Mar 04 2008
%E More terms from _N. J. A. Sloane_, Mar 05 2008
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