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%I #17 Oct 14 2022 07:13:33
%S 1,1,1,3,23,431,13935,556062
%N Number of combinatorial types of neighborly 4-polytopes with n vertices.
%D B. Gruenbaum, Convex Polytopes, 2nd Edition, p. 129a.
%H Djordje Baralić and Lazar Milenković, <a href="https://arxiv.org/abs/1704.05932">Surprising Examples of Manifolds in Toric Topology!</a>, arXiv:1704.05932 [math.AT], 2017.
%H Djordje Baralić and Lazar Milenković, <a href="https://doi.org/10.1007/s00009-022-01989-5">Small Covers and Quasitoric Manifolds over Neighborly Polytopes</a>, Mediterr. J. Math. 19, 87 (2022).
%H Moritz Firsching, <a href="https://arxiv.org/abs/1508.02531">Realizability and inscribability for simplicial polytopes via nonlinear optimization</a>, arXiv:1508.02531 [math.MG], 2015.
%H Firsching, Moritz <a href="https://doi.org/10.1007/s10107-017-1120-0">Realizability and inscribability for simplicial polytopes via nonlinear optimization</a>. Math. Program. 166, No. 1-2 (A), 273-295 (2017). Table 1
%H Moritz Firsching, <a href="https://arxiv.org/abs/1803.05205">The complete enumeration of 4-polytopes and 3-spheres with nine vertices</a>, arXiv:1803.05205 [math.MG], 2018.
%H Moritz Firsching, <a href="https://page.mi.fu-berlin.de/moritz/polytopes">Classifications and realizations</a>; <a href="https://firsching.ch/polytopes">alternative link</a>
%Y Cf. A005841, A222318.
%K nonn,more
%O 5,4
%A Gabriel Cunningham (oeis(AT)gabrielcunningham.com), Oct 19 2007
%E a(11)-a(12) from Moritz Firsching's page added by _Andrey Zabolotskiy_, Dec 24 2021
%E a(12) corrected from 556061 to 556062 based on Baralić & Milenković's paper. Apparently earlier I misinterpreted Firsching's data. - _Andrey Zabolotskiy_, Aug 27 2022
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