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A028475
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Total number of Hamiltonian cycles avoiding the root-edge in rooted cubic bipartite planar maps with 2n nodes.
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1, 4, 20, 114, 712, 4760, 33532, 246146, 1867556, 14557064, 116038672, 942597638, 7781117632, 65131605840, 551825148660, 4725380142050, 40848069782932, 356094155836640, 3127831256055624, 27662285924478844
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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LINKS
| E. Guitter, C. Kristjansen and J. L. Nielsen, Hamiltonian cycles on random Eulerian triangulations, 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
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A000356, A003122, A007084.
Sequence in context: A081085 A192624 A108447 * A128327 A171802 A100034
Adjacent sequences: A028472 A028473 A028474 * A028476 A028477 A028478
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KEYWORD
| nonn
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AUTHOR
| Valery Liskovets (liskov(AT)im.bas-net.by), Apr 29 2002
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