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Triangle T(n, d) = the number of isomorphism classes of smooth Fano d-polytopes with n vertices, read by rows (n >= 2, 1 <= d < n).
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%I #26 Sep 22 2021 07:43:26

%S 1,0,1,0,2,1,0,1,4,1,0,1,7,9,1,0,0,4,28,15,1,0,0,2,47,91,26,1,0,0,0,

%T 27,268,257,40,1,0,0,0,10,312,1318,643,62,1,0,0,0,1,137,2807,5347,

%U 1511,91,1,0,0,0,1,35,2204,19516,19453,3331

%N Triangle T(n, d) = the number of isomorphism classes of smooth Fano d-polytopes with n vertices, read by rows (n >= 2, 1 <= d < n).

%H Mikkel Obro, <a href="https://arXiv.org/abs/0704.0049">An algorithm for the classification of smooth Fano polytopes</a>, arXiv:0704.0049 [math.CO], Apr 02 2007, p. 15.

%H Mikkel Ă˜bro, <a href="https://pure.au.dk/ws/files/41742384/imf_phd_2008_moe.pdf">Classification of smooth Fano polytopes</a>, PhD thesis, 2007. See Appendix A.

%H Andreas Paffenholz, <a href="https://polymake.org/polytopes/paffenholz/www/fano.html">Smooth Reflexive Lattice Polytopes</a>

%e Table begins:

%e n |d=1|d=2|d=3|d=4|d=5|d=6|d=7

%e 1 |

%e 2 | 1 |

%e 3 | | 1 |

%e 4 | | 2 | 1 |

%e 5 | | 1 | 4 | 1 |

%e 6 | | 1 | 7 | 9 | 1 |

%e 7 | | | 4 | 28| 15| 1 |

%e 8 | | | 2 | 47| 91| 26| 1

%e 9 | | | | 27|268|257| 40

%Y Column sums are A140296.

%K nonn,tabl

%O 2,5

%A _Jonathan Vos Post_, Apr 03 2007

%E Edited and leading zeroes in rows and few more values added by _Andrey Zabolotskiy_, Sep 19 2018