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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
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, based on an email from Sascha Kurz, Mar 05 2008
STATUS
approved