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A187015 The number of different classes of the 2-dimensional convex lattice polytopes P where the convex hull of P has volume n/2. 0
1, 2, 3, 7, 6, 13, 11, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is given, using Pick's theorem, in the table, p.7 of Liu, variable v(d=2,n).

Lattice polytopes up to the equivalence relation used here are also called toric diagrams, see references below. - Andrey Zabolotskiy, May 10 2019

LINKS

Table of n, a(n) for n=1..8.

Sebastián Franco, Yang-Hui He, Chuang Sun and Yan Xiao, A comprehensive survey of brane tilings, Int. J. Mod. Phys. A, 32 (2017), 1750142, arXiv:1702.03958 [hep-th].

Heling Liu, Chuanming Zong, On the classification of convex lattice polytopes, Adv. Geom., 11 (2011), 711-729, arXiv:1103.0103 [math.MG].

Yan Xiao, Quivers, Tilings and Branes, City, University of London, 2018. See Tables 3.2-3.7.

CROSSREFS

Cf. A126587, A003051 (triangular toric diagrams only).

Sequence in context: A277902 A098285 A019585 * A245467 A070964 A111075

Adjacent sequences:  A187012 A187013 A187014 * A187016 A187017 A187018

KEYWORD

nonn,more

AUTHOR

Jonathan Vos Post, Mar 01 2011

EXTENSIONS

a(8) from Yan Xiao added by Andrey Zabolotskiy, May 10 2019

STATUS

approved

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Last modified March 8 11:15 EST 2021. Contains 341948 sequences. (Running on oeis4.)