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 A135708 Minimal total number of edges in a polyhex consisting of n hexagonal cells. 5

%I

%S 6,11,15,19,23,27,30,34,38,41,45,48,52,55,59,62,66,69,72,76,79,83,86,

%T 89,93,96,99,103,106,109,113,116,119,123,126,129,132,136,139,142,146,

%U 149,152,155,159,162,165,168,172,175,178,181,185,188,191,194,198,201,204,207,210

%N Minimal total number of edges in a polyhex consisting of n hexagonal cells.

%C The extremal examples were described by Y. S. Kupitz in 1991.

%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 G. C. Greubel, <a href="/A135708/b135708.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 3*n + ceiling(sqrt(12*n - 3)). - H. Harborth

%F 2*a(n) - A135711(n) = 6n. - _Tanya Khovanova_, Mar 07 2008

%t Table[3*n + Ceiling[Sqrt[12*n - 3]], {n,1,25}] (* _G. C. Greubel_, Oct 29 2016 *)

%o (MAGMA) [3*n+Ceiling(Sqrt(12*n-3)): n in [1..65]]; // _Vincenzo Librandi_, Oct 30 2016

%o (PARI) a(n) = 3*n + ceil(sqrt(12*n-3)); \\ _Michel Marcus_, Oct 30 2016

%Y Cf. A135711.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, based on an email from _Sascha Kurz_, Mar 05 2008

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)