

A112675


Number of directed Hamiltonian paths on a triangular grid, n vertices on each side.


6



1, 6, 24, 228, 3936, 132624, 8762040, 1156532424, 306700450536, 164818597404924, 180360080611682424, 403600060221250880496, 1853096813379189131728692, 17504763708306471241857275208
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OFFSET

1,2


COMMENTS

This sequence counts paths in a triangular region of the familiar 2dimensional lattice in which each point has 6 neighbors (sometimes called either the "triangular" or the "hexagonal" lattice), visiting every vertex of the region exactly once. The paths are not assumed to be closed. A path and its reversal are not considered equivalent.


LINKS

Table of n, a(n) for n=1..14.
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Triangular Grid Graph
Index entries for sequences related to graphs, Hamiltonian


CROSSREFS

Cf. A003763, A112676.
Sequence in context: A091097 A231317 A223105 * A052583 A052671 A052733
Adjacent sequences: A112672 A112673 A112674 * A112676 A112677 A112678


KEYWORD

more,nonn


AUTHOR

Gareth McCaughan (gareth.mccaughan(AT)pobox.com), Dec 30 2005


EXTENSIONS

a(8)a(14) from Andrew Howroyd, Nov 02 2015


STATUS

approved



