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

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

Offset

1,2

Links

Table of n, a(n) for n=1..9.

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

Crossrefs

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

Sequence in context: A036688 A009348 A009365 * A278172 A204252 A281564

Adjacent sequences: A140293 A140294 A140295 * A140297 A140298 A140299

Keyword

hard,more,nonn

Author

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

Extensions

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

Status

approved