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%I #27 Jul 01 2020 13:00:25
%S 1,2,6,25,138,972,8477,89405,1119280,16384508,276961252,5349351298,
%T 116985744912,2873993336097,78768494976617
%N Number of triangulations of cyclic 3-polytope C(3,n+3).
%C a(n) is also the number of persistent graphs on n+1 vertices. - _Malte Renken_, Jun 30 2020
%D J. Rambau and F. Santos, The Baues problem for cyclic polytopes I, In "Special issue on Combinatorics of convex polytopes" (K. Fukuda and G. M. Ziegler, eds.), European J. Combin. 21:1 (2000), 65-83.
%D TOPCOM: Triangulations of Point Configurations and Oriented Matroids (ZIB Report 02-17). Proceedings of the International Congress of Mathematical Software ICMS 2002.
%H C. A. Athanasiadis, J. A. De Loera, V. Reiner and F. Santos, <a href="http://personales.unican.es/santosf/Articulos/">Fiber polytopes for the projections between cyclic polytopes</a>, European Journal of Combinatorics, Volume: 21, Issue: 1, 2000, pp. 19 - 47.
%H M. Azaola and F. Santos, <a href="http://personales.unican.es/santosf/Articulos/">The number of triangulations of the cyclic polytope C(n,n-4)</a>, Discrete Comput. Geom., 27 (2002), 29-48.
%H Vincent Froese, Malte Renken, <a href="https://arxiv.org/abs/1911.05012">Persistent Graphs and Cyclic Polytope Triangulations</a>, arXiv:1911.05012 [cs.DM], 2020. See Table 1.
%H Michael Joswig, Lars Kastner, <a href="https://arxiv.org/abs/1804.08029">New counts for the number of triangulations of cyclic polytopes</a>, arXiv:1804.08029 [math.CO], 2018. See Table 1 p. 7.
%H J. Rambau, <a href="http://www.rambau.wm.uni-bayreuth.de/TOPCOM/">TOPCOM</a>
%o (TOPCOM) cyclic 14 3 | points2ntriangs -v
%Y Cf. A028441.
%K hard,nonn
%O 1,2
%A reiner(AT)math.umn.edu (Victor Reiner), edelman(AT)math.umn.edu (Paul Edelman)
%E a(8) and a(9) computed by J. Rambau.
%E a(7) corrected and a(10) computed by _Jörg Rambau_, Sep 19 2006, using the TOPCOM software.
%E Typo in a(8) fixed and a(11) computed using the TOPCOM software by _Jörg Rambau_, Aug 11 2011
%E a(12) (computed by Joswig & Kastner) from _Michel Marcus_, Apr 23 2018
%E a(13) to a(15) (computed by Froese & Renken) from _Malte Renken_, Jun 30 2020
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