

A135711


Minimal perimeter of a polyhex with n cells.


4



6, 10, 12, 14, 16, 18, 18, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 30, 32, 32, 34, 34, 34, 36, 36, 36, 38, 38, 38, 40, 40, 40, 42, 42, 42, 42, 44, 44, 44, 46, 46, 46, 46, 48, 48, 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
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OFFSET

1,1


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

Table of n, a(n) for n=1..72.


FORMULA

It is easy to use the formula of Harborth given in A135708 to show that a(n) = 2*ceiling(sqrt(12*n3)).  Sascha Kurz, Mar 05 2008
2*A135708(n)  a(n) = 6n.  Tanya Khovanova, Mar 07 2008


MATHEMATICA

Table[2Ceiling[Sqrt[12n3]], {n, 120}] (* Harvey P. Dale, Dec 29 2019 *)


CROSSREFS

Cf. A000228 = number of hexagonal polyominoes (or planar polyhexes) with n cells; A135708.
Analogs for triangles, squares, cubes: A067628, A027709, A075777.
Sequence in context: A082300 A050703 A330397 * A161543 A056868 A069209
Adjacent sequences: A135708 A135709 A135710 * A135712 A135713 A135714


KEYWORD

nonn


AUTHOR

Tanya Khovanova, Mar 04 2008


EXTENSIONS

More terms from N. J. A. Sloane, Mar 05 2008


STATUS

approved



