OFFSET
0,2
COMMENTS
a(n) is a sharp upper bound of the number of vertices of the polytope of the n X n X n stochastic tensors, or equivalently, of the number of Latin squares of order n, or equivalently, of the number of n X n X n line-stochastic (0,1)-tensors (see Zhang et al.).
LINKS
Fuzhen Zhang and Xiao-Dong Zhang, Enumerating extreme points of the polytopes of stochastic tensors: an optimization approach, Optimization, 69:4, 729-741, (2020). arXiv:2008.04655 [math.CO], 2020. See p. 6.
Fuzhen Zhang and Xiao-Dong Zhang, Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors, arXiv:2110.12337 [math.CO], 2021. See p. 5.
FORMULA
MATHEMATICA
a[n_]:=Binomial[n^3+3n^2-3n+1, n^3]; Array[a, 8, 0]
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 20 2021
STATUS
approved