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A186866
Number of 7-step king's tours on an n X n board summed over all starting positions.
1
0, 0, 2984, 68272, 296360, 722384, 1335984, 2129440, 3102752, 4255920, 5588944, 7101824, 8794560, 10667152, 12719600, 14951904, 17364064, 19956080, 22727952, 25679680, 28811264, 32122704, 35614000, 39285152, 43136160, 47167024
OFFSET
1,3
COMMENTS
From J. Volkmar Schmidt, Oct 24 2023 (Start)
Proof of a(n) follows proof scheme from David A. Corneth for A186864.
Distribution matrix of surrounding rectangles for 7-step walks is:
[0 0 0 0 0 0 2]
[0 0 0 800 1600 1024 252]
[0 0 2984 9780 7904 3360 644]
[0 800 9780 12416 6636 2272 388]
[0 1600 7904 6636 2912 864 136]
[0 1024 3360 2272 864 224 32]
[2 252 644 388 136 32 4]
(End)
FORMULA
Empirical: a(n) = 89928*n^2 - 555464*n + 817760 for n>5.
EXAMPLE
Some solutions for 3X3
..0..2..1....0..2..0....6..0..0....1..7..6....1..2..3....7..2..1....6..5..0
..4..3..0....3..7..1....7..5..2....2..0..5....0..4..7....3..6..0....7..4..1
..5..6..7....4..5..6....4..3..1....3..4..0....0..6..5....5..4..0....0..2..3
CROSSREFS
Row 7 of A186861.
Sequence in context: A235503 A120373 A365258 * A252571 A231628 A231623
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 27 2011
STATUS
approved