|
Search: id:A126026
|
|
|
| A126026 |
|
Conjectured upper bound on area of the convex hull of any edge-to-edge connected system of regular unit hexagons (n-polyhexes). |
|
+0
1
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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
|
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.
|
|
CROSSREFS
|
Cf. A000228, A036359, A002216, A005963, A000228, A001998, A018190, A001207, A057973, A122133.
Sequence in context: A115793 A076614 A000549 this_sequence A057129 A036404 A018498
Adjacent sequences: A126023 A126024 A126025 this_sequence A126027 A126028 A126029
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 27 2007
|
|
|
Search completed in 0.002 seconds
|
