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A028475 Total number of Hamiltonian cycles avoiding the root-edge in rooted cubic bipartite planar maps with 2n nodes. 1
1, 4, 20, 114, 712, 4760, 33532, 246146, 1867556, 14557064, 116038672, 942597638, 7781117632, 65131605840, 551825148660, 4725380142050, 40848069782932, 356094155836640, 3127831256055624, 27662285924478844, 246164019830290392, 2203001550262470312, 19817596934324929372, 179122742853479945254, 1626121500460666711772, 14822276313411258015520, 135615436173317732453408, 1245149962077083336891292, 11469647289793201572263720, 105974634025908284618398424, 981959564213395629385138012, 9123241004157603739262143522 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..32.

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


a(n) = A116456(n) / 2. - Sean A. Irvine, Feb 01 2020


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.


Cf. A000356, A003122, A007084, A116456.

Sequence in context: A287512 A211248 A346414 * A128327 A320615 A316298

Adjacent sequences: A028472 A028473 A028474 * A028476 A028477 A028478




Valery A. Liskovets, Apr 29 2002



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Last modified December 1 15:30 EST 2022. Contains 358468 sequences. (Running on oeis4.)