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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 (list; graph; refs; listen; history; text; internal format)
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 (gareth.mccaughan(AT)pobox.com), Dec 30 2005

EXTENSIONS

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

STATUS

approved

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Last modified June 12 07:43 EDT 2021. Contains 344943 sequences. (Running on oeis4.)