A127709 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).

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, 27, 268, 257, 40, 1, 0, 0, 0, 10, 312, 1318, 643, 62, 1, 0, 0, 0, 1, 137, 2807, 5347, 1511, 91, 1, 0, 0, 0, 1, 35, 2204, 19516, 19453, 3331

Offset

2,5

Links

Table of n, a(n) for n=2..65.

Mikkel Obro, An algorithm for the classification of smooth Fano polytopes, arXiv:0704.0049 [math.CO], Apr 02 2007, p. 15.

Mikkel Øbro, Classification of smooth Fano polytopes, PhD thesis, 2007. See Appendix A.

Andreas Paffenholz, Smooth Reflexive Lattice Polytopes

Example

Table begins:
n  |d=1|d=2|d=3|d=4|d=5|d=6|d=7
1  |
2  | 1 |
3  |   | 1 |
4  |   | 2 | 1 |
5  |   | 1 | 4 | 1 |
6  |   | 1 | 7 | 9 | 1 |
7  |   |   | 4 | 28| 15| 1 |
8  |   |   | 2 | 47| 91| 26| 1
9  |   |   |   | 27|268|257| 40

Crossrefs

Column sums are A140296.

Sequence in context: A116088 A136501 A180983 * A343730 A343761 A336423

Adjacent sequences: A127706 A127707 A127708 * A127710 A127711 A127712

Keyword

nonn,tabl

Author

Jonathan Vos Post, Apr 03 2007

Extensions

Edited and leading zeroes in rows and few more values added by Andrey Zabolotskiy, Sep 19 2018

Status

approved