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A186861
Array read by antidiagonals: T(n,k) is the number of n-step king's tours on a k X k board summed over all starting positions.
8
1, 4, 0, 9, 12, 0, 16, 40, 24, 0, 25, 84, 160, 24, 0, 36, 144, 408, 496, 0, 0, 49, 220, 768, 1764, 1208, 0, 0, 64, 312, 1240, 3768, 6712, 2240, 0, 0, 81, 420, 1824, 6508, 17280, 22672, 2984, 0, 0, 100, 544, 2520, 9984, 32520, 74072, 68272, 2384, 0, 0, 121, 684
OFFSET
1,2
COMMENTS
Table starts
1 4 9 16 25 36 49 64 81 100
0 12 40 84 144 220 312 420 544 684
0 24 160 408 768 1240 1824 2520 3328 4248
0 24 496 1764 3768 6508 9984 14196 19144 24828
0 0 1208 6712 17280 32520 52432 77016 106272 140200
0 0 2240 22672 74072 156484 268048 408764 578632 777652
0 0 2984 68272 296360 722384 1335984 2129440 3102752 4255920
0 0 2384 183472 1110000 3193800 6481216 10899404 16418600 23038804
0 0 784 436984 3908376 13530576 30543072 54738536 85743256
0 0 0 905776 12956800 55056168 139775784
LINKS
FORMULA
Empirical, for all rows: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3,3,3,5,6,7,8,9 respectively for row=1..8.
EXAMPLE
Some n=3 solutions for 3 X 3:
3 2 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 1 0
1 0 0 1 0 0 0 2 0 1 2 0 2 3 0 0 2 0 2 0 0
0 0 0 2 3 0 0 0 1 3 0 0 0 1 0 0 0 3 0 3 0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 27 2011
STATUS
approved