A112675 Number of directed Hamiltonian paths on a triangular grid, n vertices on each side.

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

Offset

1,2

Comments

This sequence counts paths in a triangular region of the familiar 2-dimensional 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, Dec 30 2005

Extensions

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

Status

approved