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A135711
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Minimal perimeter of a polyhex with n cells.
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5
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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
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1,1
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REFERENCES
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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.
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LINKS
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Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, Extremal {p, q}-Animals, Ann. Comb. (2023). See Corollary 1.9 at p. 8.
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FORMULA
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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
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MATHEMATICA
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Table[2Ceiling[Sqrt[12n-3]], {n, 120}] (* Harvey P. Dale, Dec 29 2019 *)
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CROSSREFS
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Cf. A000228 (number of hexagonal polyominoes (or planar polyhexes) with n cells), A135708.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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