

A135708


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


5



6, 11, 15, 19, 23, 27, 30, 34, 38, 41, 45, 48, 52, 55, 59, 62, 66, 69, 72, 76, 79, 83, 86, 89, 93, 96, 99, 103, 106, 109, 113, 116, 119, 123, 126, 129, 132, 136, 139, 142, 146, 149, 152, 155, 159, 162, 165, 168, 172, 175, 178, 181, 185, 188, 191, 194, 198, 201, 204, 207, 210
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OFFSET

1,1


COMMENTS

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


REFERENCES

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: NorthHolland: Colloq. Math. Soc. Janos Bolyai. 63, 217244.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = 3*n + ceiling(sqrt(12*n  3)).  H. Harborth
2*a(n)  A135711(n) = 6n.  Tanya Khovanova, Mar 07 2008


MATHEMATICA

Table[3*n + Ceiling[Sqrt[12*n  3]], {n, 1, 25}] (* G. C. Greubel, Oct 29 2016 *)


PROG

(MAGMA) [3*n+Ceiling(Sqrt(12*n3)): n in [1..65]]; // Vincenzo Librandi, Oct 30 2016
(PARI) a(n) = 3*n + ceil(sqrt(12*n3)); \\ Michel Marcus, Oct 30 2016


CROSSREFS

Cf. A135711.
Sequence in context: A043098 A039276 A044995 * A315395 A315396 A315397
Adjacent sequences: A135705 A135706 A135707 * A135709 A135710 A135711


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, based on an email from Sascha Kurz, Mar 05 2008


STATUS

approved



