A309579 Maximum principal ratio of a strongly connected digraph on n nodes.

2, 6, 22, 102, 582, 3942, 30822, 272742, 2691942, 29303142, 348637542, 4499984742, 62618845542, 934401757542, 14882928349542, 252007880413542, 4520257017565542, 85616990623453542, 1707551662741213542, 35768179777214173542, 785101998295619293542, 18019779824218937053542

Offset: 3

Author

Sinan G. Aksoy, Aug 08 2019

Keywords

• nonn

Comments

The principal ratio of a strongly connected digraph is the ratio of largest to smallest entries in the stationary distribution of a simple random walk on that digraph.

Links

• S. Aksoy, F. Chung, X. Peng, Extreme values of the stationary distribution of random walks on directed graphs, arXiv:1602.01162 [math.CO], 2016.
• S. Aksoy, F. Chung, X. Peng, Extreme values of the stationary distribution of random walks on directed graphs, Advances in Applied Mathematics, 81:128--155, 2016.

Crossrefs

Cf. A056199.

Programs

PARI

a(n) = (2/3) * (n-1)! * ( n/(n-1) + (1/(n-1)!) * sum(i=1, n-3, i!)); \\ Michel Marcus, Aug 11 2019

Formula

a(n) = (2/3) * (n-1)! * ( n/(n-1) + (1/(n-1)!) * Sum_{i=1..n-3} i! ).

a(n) = 2 * A056199(n-1). - Alois P. Heinz, Aug 11 2019