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%I #40 Apr 20 2024 07:41:13
%S 5,7,18,13,33,26,45,27,51,51,67,53,69,74,133,48,89,81,102,110,178,105,
%T 124,109,161,119,164,135,142,187,140,105,274,159,383,169,145,166,329,
%U 221,177,266,180,230,404,189,220,213,315,264,384,233,225,260,573,298
%N Number of isomorphism classes of rank one toric log del Pezzo surfaces with index L = n.
%C A145581(n) is the number of toric log del Pezzo surfaces with index L = n. Both are in the table for Theorem 1.2, p. 4 of Kasprzyk, Kreuzer and Nill.
%H Justus Springer, <a href="/A145582/b145582.txt">Table of n, a(n) for n = 1..5000</a>
%H Andreas Bäuerle, <a href="https://arxiv.org/abs/2308.12719">Sharp volume and multiplicity bounds for Fano simplices</a>, arXiv:2308.12719 [math.CO], 2023.
%H Andreas Bäuerle, <a href="https://github.com/abaeuerle/fano-simplices">Classification of Fano simplices</a>
%H Daniel Haettig, Beatrice Hafner, Juergen Hausen and Justus Springer, <a href="https://arxiv.org/abs/2207.14790">Del Pezzo surfaces of Picard number one admitting a torus action</a>, arXiv:2207.14790 [math.AG], 2022. [see Proposition 7.1, p. 27]
%H Daniel Hättig, Jürgen Hausen, Justus Springer and Hendrik Süß, <a href="https://www.math.uni-tuebingen.de/forschung/algebra/ldp-database/">Log del Pezzo surfaces with torus action - a searchable database</a>
%H Alexander M. Kasprzyk, Maximilian Kreuzer and Benjamin Nill, <a href="https://doi.org/10.1112/S1461157008000387">On the combinatorial classification of toric log del Pezzo surfaces</a>, LMS J. Comput. Math. 13 (2010) 33-46; arXiv:<a href="https://arxiv.org/abs/0810.2207">0810.2207</a> [math.AG], 2008.
%H Alexander M. Kasprzyk and Benjamin Nill, Chapter 17 <a href="https://doi.org/10.1142/9789814412551_0017">Fano polytopes</a>, in: Strings, Gauge Fields, And The Geometry Behind, World Scientific, 2012. See p. 359.
%Y Cf. A145581, A364712.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Oct 14 2008
%E a(17) from Kasprzyk and Nill (2012) added by _Andrey Zabolotskiy_, Feb 17 2020
%E a(18)-a(200) from Haettig, Hafner, Hausen and Springer (2022) added by _Justus Springer_, Aug 04 2023
%E a(201)-a(1000) from Bäuerle's data, added by _Andrey Zabolotskiy_, Oct 01 2023
%E a(1001)-a(5000) computed using Bäuerle's algorithm, added by _Justus Springer_, Apr 15 2024