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A227301 Number of Hamiltonian circuits in a 2n node X 2n node square lattice, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 8 elements. 4
0, 0, 121, 578937, 58407351059, 134528360800075421, 7015812452559988037073365, 8235314565328229497795808499821534, 216740797236120772990968348272561831275923059, 127557553423846099192878370706037904215158660401579043097 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
EXAMPLE
When n = 3 there are 121 Hamiltonian circuits in a 6 X 6 square lattice where the orbits under the symmetry group of the square have 8 elements. One of these circuits is shown below with its 8 distinct transformations under rotation and reflection:
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__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__o o o o o__o o__o__o__o o o o o__o o
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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__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__o o o o
| | | | | | | |
o__o__o__o__o__o o__o o__o o__o
CROSSREFS
Sequence in context: A135825 A221392 A337728 * A261364 A317956 A136094
KEYWORD
nonn,hard
AUTHOR
EXTENSIONS
a(4) from Giovanni Resta, Jul 11 2013
a(5)-a(10) from Ed Wynn, Feb 05 2014
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)