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A227005
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 2 elements.
6
0, 1, 4, 20, 346, 6891, 634172, 47917598, 27622729933, 6998287399637
OFFSET
1,3
FORMULA
a(2n) = A237431(2n), a(2n+1) = A237431(2n+1) + A237432(n+1). - 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 2 elements. The 2 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
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