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A328341
Number of geometrically distinct open knight's tours on a 4 X n chessboard.
3
0, 0, 3, 0, 22, 186, 1603, 7772, 47478, 303278, 1671273, 9121582, 50322028, 270896326, 1426536267, 7454807822, 38607660199, 197696949844, 1003736587788, 5060326202622, 25334034892953, 126024078250318, 623383415637750, 3067618264121349, 15022847233751804, 73245459228339114
OFFSET
1,3
FORMULA
a(2*n) = A123936(2*n)/2; a(2*n-1) = (A123936(2*n-1) + A328340(n))/2.
EXAMPLE
a(3) = 3 because there are two symmetric and one asymmetric tour:
+----+----+----+----+ +----+----+----+----+ +----+----+----+----+
| 8 | 11 | 6 | 3 | | 1 | 4 | 7 | 10 | | 1 | 4 | 7 | 10 |
+----+----+----+----+ +----+----+----+----+ +----+----+----+----+
| 1 | 4 | 9 | 12 | | 8 | 11 | 2 | 5 | | 12 | 9 | 2 | 5 |
+----+----+----+----+ +----+----+----+----+ +----+----+----+----+
| 10 | 7 | 2 | 5 | | 3 | 6 | 9 | 12 | | 3 | 6 | 11 | 8 |
+----+----+----+----+ +----+----+----+----+ +----+----+----+----+
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 12 2019
STATUS
approved