cp's OEIS Frontend

A028475 Total number of Hamiltonian cycles avoiding the root-edge in rooted cubic bipartite planar maps with 2n nodes.

%I A028475 #35 Dec 10 2023 14:34:39
%S A028475 1,4,20,114,712,4760,33532,246146,1867556,14557064,116038672,
%T A028475 942597638,7781117632,65131605840,551825148660,4725380142050,
%U A028475 40848069782932,356094155836640,3127831256055624,27662285924478844,246164019830290392,2203001550262470312,19817596934324929372
%N A028475 Total number of Hamiltonian cycles avoiding the root-edge in rooted cubic bipartite planar maps with 2n nodes.
%C A028475 An algorithm for calculating these numbers is known. 2*a(n) can be interpreted as the number of pairs of non-intersecting arch configurations (over and under a straight line) connecting 2n points in the line, where all points are marked + and - alternately, every point belongs to a unique arch and the ends of every arch have different signs.
%H A028475 Olivier Golinelli, <a href="/A028475/b028475.txt">Table of n, a(n) for n = 1..34</a>
%H A028475 E. Guitter, C. Kristjansen and J. L. Nielsen, <a href="https://arxiv.org/abs/cond-mat/9811289">Hamiltonian cycles on random Eulerian triangulations</a>, arXiv:cond-mat/9811289 [cond-mat.stat-mech], 1998; Nucl.Phys. B546 (1999), No.3, 731-750.
%H A028475 James A. Sellers, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Sellers/sellers4.html">Domino Tilings and Products of Fibonacci and Pell Numbers</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2.
%F A028475 a(n) = A116456(n) / 2. - _Sean A. Irvine_, Feb 01 2020
%e A028475 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.
%Y A028475 Cf. A000356, A003122, A007084, A116456.
%K A028475 nonn,hard
%O A028475 1,2
%A A028475 _Valery A. Liskovets_, Apr 29 2002
%E A028475 a(21)-a(32) from _Cyril Banderier_, Nov 06 2022