A090045 -id:A090045 - cp's OEIS frontend

A140296 Number of isomorphism classes of smooth toric Fano n-folds (or, equivalently, regular Fano n-topes).

Original entry on oeis.org

1, 5, 18, 124, 866, 7622, 72256, 749892, 8229721

Offset: 1

Alexander M Kasprzyk (kasprzyk(AT)unb.ca), Jun 23 2008

Victor V. Batyrev, Toric Fano threefolds, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), no. 4, 704-717, 927.
Yang-Hui He, Rak-Kyeong Seong, and Shing-Tung Yau, Calabi-Yau Volumes and Reflexive Polytopes, arXiv:1704.03462 [hep-th], 2017.
Maximillian Kreuzer and Benjamin Nill, Classification of toric fano 5-folds, arXiv:math/0702890 [math.AG], 2007.
Benjamin Lorenz and Benjamin Nill, Smooth Gorenstein polytopes
Mikkel Oebro, An algorithm for the classification of smooth Fano polytopes, arXiv:0704.0049 [math.CO], 2007.
Mikkel Oebro, Text-format and PALP-friendly files containing the classifications up to n=7
Andreas Paffenholz, Smooth Reflexive Lattice Polytopes

See A090045 for all the reflexive polytopes. Cf. A127709.

a(9) from F. Chapoton, Mar 13 2014

A141682 Number of isomorphism classes of (2n+1)-reflexive polygons.

Original entry on oeis.org

16, 1, 12, 29, 1, 61, 81, 1, 113, 131, 2, 163, 50, 2, 215, 233, 2, 34, 285, 3, 317, 335, 2, 367, 182, 3, 419, 72, 4, 469, 489, 3, 93, 539, 4, 571, 591, 3, 185, 641, 5, 673, 131, 5, 725, 240, 6, 148, 795, 5, 827, 845, 3, 877, 897, 7, 929, 186, 6, 338, 656, 7, 240, 1049, 8, 1081, 393, 5, 1133, 1151, 8, 542, 245, 7, 1235, 1253

Offset: 0

Benjamin Nill, Jul 02 2012

nonn

There are no l-reflexive polygons for even index l.

			a(0)=16 equals the number of isomorphism classes of (1-)reflexive polygons, A090045(2).

Andrey Zabolotskiy, Table of n, a(n) for n = 0..99 (from the Graded Ring Database)
Dimitrios I. Dais, On the Twelve-Point Theorem for l-Reflexive Polygons, arXiv:1806.08351 [math.CO], 2018.
A. M. Kasprzyk and B. Nill, Reflexive polytopes of higher index and the number 12, arXiv:1107.4945 [math.AG], 2011.
A. M. Kasprzyk and B. Nill, Toric l-reflexive surfaces at Graded Ring Database.

Cf. A090045.

It seems that for n > 2, a(n) = 17*n - k where k = 21, 22, 23, 24 iff 2*n+1 is a prime from A068228, A068229, A040117, A068231, respectively. - Andrey Zabolotskiy, Apr 21 2022

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A140296 Number of isomorphism classes of smooth toric Fano n-folds (or, equivalently, regular Fano n-topes).

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A141682 Number of isomorphism classes of (2n+1)-reflexive polygons.

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