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 A349512 a(n) = binomial(n^3 + 3*n^2 - 3*n + 1, n^3). 6
 1, 2, 6435, 4154246671960, 5397234129638871133346507775, 80240648651400365471854502514501453704175376562496, 54198670627270688013781273396239242514947489935351300645194042280183395324517200 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..6. 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 A349508(n)/A349509(n) <= A349510(n) < A349511(n) < a(n) (see Corollary 7 in Zhang et al., 2021). a(n) ~ C*3^(3(n - n^2))*exp(3*(3*n/2 + n^2))*n^(3(-n + n^2)), where C = e^(-15)/sqrt(54*Pi). MATHEMATICA a[n_]:=Binomial[n^3+3n^2-3n+1, n^3]; Array[a, 8, 0] CROSSREFS Cf. A000578, A229013. Cf. A349506, A349507, A349508, A349509, A349510, A349511. Sequence in context: A190127 A099690 A196750 * A107021 A107022 A330901 Adjacent sequences: A349509 A349510 A349511 * A349513 A349514 A349515 KEYWORD nonn AUTHOR Stefano Spezia, Nov 20 2021 STATUS approved

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Last modified November 28 21:44 EST 2023. Contains 367419 sequences. (Running on oeis4.)