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A126026 Conjectured upper bound on area of the convex hull of any edge-to-edge connected system of regular unit hexagons (n-polyhexes). 0
0, 1, 2, 4, 5, 8, 10, 13, 17, 20, 24, 28, 33, 38, 43, 49, 55, 61, 68, 75, 82, 90, 97, 106, 114, 123, 133, 142, 152, 162, 173, 184, 195, 207, 219, 231, 244, 257, 270, 284, 297, 312, 326, 341, 357, 372, 388, 404, 421, 438, 455, 473, 491, 509, 528, 547, 566 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Kurz proved the polyomino equivalent of this conjecture as A122133 and abstracts: "In this article we prove a conjecture of Bezdek, Brass and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of n unit hypercubes in the d-dimensional Euclidean space. For d=2 we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each n."

LINKS

Table of n, a(n) for n=1..57.

Sascha Kurz, Convex hulls of polyominoes, 26 Feb 2007, Conjecture 2, p. 12.

Eric Weisstein's World of Mathematics, Polyhex.

FORMULA

a(n) = Floor((n^2 + 14*n/3 + 1)/6).

EXAMPLE

a(10) = 24 because floor((10^2 + 14*10/3 + 1)/6) = floor(24.6111111) = 24.

MATHEMATICA

Table[Floor[(n^2+14n/3+1)/6], {n, 0, 80}] (* Harvey P. Dale, Apr 11 2012 *)

CROSSREFS

Cf. A000228, A036359, A002216, A005963, A000228, A001998, A018190, A001207, A057973, A122133.

Sequence in context: A231056 A000549 A191985 * A199425 A057129 A036404

Adjacent sequences:  A126023 A126024 A126025 * A126027 A126028 A126029

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 27 2007

EXTENSIONS

More terms from Harvey P. Dale, Apr 11 2012

STATUS

approved

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Last modified December 20 10:32 EST 2014. Contains 252241 sequences.