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A135711
Minimal perimeter of a polyhex with n cells.
5
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
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: North-Holland: Colloq. Math. Soc. Janos Bolyai. 63, 217-244.
LINKS
Li Gan, Stéphane Ouvry, and Alexios P. Polychronakos, Algebraic area enumeration of random walks on the honeycomb lattice, arXiv:2107.10851 [math-ph], 2021.
Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, Extremal {p, q}-Animals, Ann. Comb. (2023). See Corollary 1.9 at p. 8.
FORMULA
It is easy to use the formula of Harborth given in A135708 to show that a(n) = 2*ceiling(sqrt(12*n-3)). - Sascha Kurz, Mar 05 2008
2*A135708(n) - a(n) = 6n. - Tanya Khovanova, Mar 07 2008
MATHEMATICA
Table[2Ceiling[Sqrt[12n-3]], {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: A361126 A330397 A371933 * A161543 A056868 A069209
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Mar 04 2008
EXTENSIONS
More terms from N. J. A. Sloane, Mar 05 2008
STATUS
approved