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

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

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: North-Holland: Colloq. Math. Soc. Janos Bolyai. 63, 217-244.

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*n-3)): n in [1..65]]; // Vincenzo Librandi, Oct 30 2016
(PARI) a(n) = 3*n + ceil(sqrt(12*n-3)); \\ Michel Marcus, Oct 30 2016
(Python)
from math import isqrt
def A135708(n): return 3*n+1+isqrt(12*n-4) # Chai Wah Wu, Jul 28 2022

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