A265914 Number of Hamiltonian paths on an n X n grid reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

1, 1, 3, 38, 549, 28728, 1692417, 377919174, 93177169027, 91255604983167, 98333935794279062, 431583106977641773651, 2081500714709464758363648, 41476136050841717002906372881, 907951420995033325255530074961505, 82829339673122474155192677008453291270

Offset: 1

Author

Luca Petrone, Dec 18 2015

Keywords

• nonn
• walk
• hard

Comments

For odd n > 1 the only symmetry possible is rotation by 180 degrees. For even n the only symmetries are reflections either horizontally or vertically. - Andrew Howroyd, Apr 15 2016

Links

• Oliver R. Bellwood, Heitor P. Casagrande, and William J. Munro, Fractal Path Strategies for Efficient 2D DMRG Simulations, arXiv:2507.11820 [cond-mat.str-el], 2025. See p. 5.
• Jean-Marc Mayer, Claude Guez, and Jean Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990.

Crossrefs

Cf. A120443, A209077, A068393.

Extensions

a(9)-a(15) from Andrew Howroyd, Apr 15 2016

a(16) from Oliver R. Bellwood, Jun 06 2025