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A227257
Number of Hamiltonian circuits in a 2n X 2n square lattice of nodes, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 4 elements.
6
0, 1, 24, 1760, 411861, 551247139, 2883245852086, 85948329517780776, 11001968794030973784902, 7462399462450938863305238264
OFFSET
1,3
FORMULA
a(n) = A237429(n) + A237430(n). - Ed Wynn, Feb 07 2014
EXAMPLE
When n = 2, there is only 1 Hamiltonian circuit in a 4 X 4 square lattice, where the orbits under the symmetry group of the square have 4 elements. The 4 elements are:
o__o__o__o o__o__o__o o__o__o__o o__o o__o
| | | | | | | | | |
o o__o__o o o__o o o__o__o o o o o o
| | | | | | | | | | | |
o o__o__o o o o o o__o__o o o o__o o
| | | | | | | | | |
o__o__o__o o__o o__o o__o__o__o o__o__o__o
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(4) from Giovanni Resta, Jul 11 2013
a(5)-a(10) from Ed Wynn, Feb 05 2014
STATUS
approved