

A028475


Total number of Hamiltonian cycles avoiding the rootedge in rooted cubic bipartite planar maps with 2n nodes.


2



1, 4, 20, 114, 712, 4760, 33532, 246146, 1867556, 14557064, 116038672, 942597638, 7781117632, 65131605840, 551825148660, 4725380142050, 40848069782932, 356094155836640, 3127831256055624, 27662285924478844, 246164019830290392, 2203001550262470312, 19817596934324929372
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OFFSET

1,2


COMMENTS

An algorithm for calculating these numbers is known. 2*a(n) can be interpreted as the number of pairs of nonintersecting 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.


LINKS



FORMULA



EXAMPLE

n=2. There are 3 rooted cubic bipartite planar maps with 4 nodes: a quadrangular with two nonadjacent 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 rootvertex. For the other two rootings, there are 4 rootedge avoiding Hamiltonian cycles. So a(2)=4.


CROSSREFS



KEYWORD

nonn,hard


AUTHOR



EXTENSIONS



STATUS

approved



