A028475 Total number of Hamiltonian cycles avoiding the root-edge in rooted cubic bipartite planar maps with 2n nodes.
1, 4, 20, 114, 712, 4760, 33532, 246146, 1867556, 14557064, 116038672, 942597638, 7781117632, 65131605840, 551825148660, 4725380142050, 40848069782932, 356094155836640, 3127831256055624, 27662285924478844, 246164019830290392, 2203001550262470312, 19817596934324929372
Offset: 1
Examples
n=2. There are 3 rooted cubic bipartite planar maps with 4 nodes: a quadrangular with two non-adjacent edges doubled (parallel), where one vertex and any of the edges incident to it are taken as the root. No Hamiltonian cycle can avoid the sole edge incident to the root-vertex. For the other two rootings, there are 4 root-edge avoiding Hamiltonian cycles. So a(2)=4.
Links
- Olivier Golinelli, Table of n, a(n) for n = 1..34
- E. Guitter, C. Kristjansen and J. L. Nielsen, Hamiltonian cycles on random Eulerian triangulations, arXiv:cond-mat/9811289 [cond-mat.stat-mech], 1998; Nucl.Phys. B546 (1999), No.3, 731-750.
- James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2.
Formula
a(n) = A116456(n) / 2. - Sean A. Irvine, Feb 01 2020
Extensions
a(21)-a(32) from Cyril Banderier, Nov 06 2022
Comments