%I #22 Dec 19 2022 12:08:38

%S 1,3,7,23,19,65,46,202,156,281,183,972,333,903,1029,2507,912

%N Number of six-dimensional simplical toric diagrams with hypervolume n.

%C Also gives the number of distinct abelian orbifolds of C^7/Gamma, Gamma in SU(7).

%H Gabriele Balletti, <a href="https://github.com/gabrieleballetti/small-lattice-polytopes">Dataset of "small" lattice polytopes</a>

%H J. Davey, A. Hanany and R. K. Seong, <a href="https://doi.org/10.1007/JHEP06(2010)010">Counting Orbifolds</a>, J. High Energ. Phys. (2010) 2010: 10; arXiv:<a href="https://arxiv.org/abs/1002.3609">1002.3609</a> [hep-th], 2010.

%H A. Hanany and R. K. Seong, <a href="https://doi.org/10.1007/JHEP01(2011)027">Symmetries of abelian orbifolds</a>, J. High Energ. Phys. (2011) 2011: 27; <a href="https://arxiv.org/abs/1009.3017">arXiv:1009.3017 [hep-th]</a>, 2010-2011.

%H Andrey Zabolotskiy, <a href="https://arxiv.org/abs/2003.10251">Coweight lattice A^*_n and lattice simplices</a>, arXiv:2003.10251 [math.CO], 2020.

%Y Cf. A003051 (No. of two-dimensional triangular toric diagrams of area n), A045790 (No. of three-dimensional tetrahedral toric diagrams of volume n), A173824 (No. of four-dimensional simplical toric diagrams of hypervolume n), A173877 (No. of five-dimensional simplical toric diagrams of hypervolume n).

%K nonn,more

%O 1,2

%A Rak-Kyeong Seong (rak-kyeong.seong(AT)imperial.ac.uk), Mar 01 2010

%E a(8)-a(16) from Balletti's data and a(17) from Table 15 of Hanany & Seong 2011 added by _Andrey Zabolotskiy_, Mar 13 2020