A186865 Number of 6-step king's tours on an n X n board summed over all starting positions.

0, 0, 2240, 22672, 74072, 156484, 268048, 408764, 578632, 777652, 1005824, 1263148, 1549624, 1865252, 2210032, 2583964, 2987048, 3419284, 3880672, 4371212, 4890904, 5439748, 6017744, 6624892, 7261192, 7926644, 8621248, 9345004, 10097912, 10879972, 11691184

Offset

1,3

Comments

From J. Volkmar Schmidt, Oct 18 2023: (Start)

Proof of a(n) = 14576*n^2 - 77924*n + 99292 for n>4 follows proof scheme from David A. Corneth for A186864.

Distribution matrix of surrounding rectangles for 6-step walks is:

[0 0 0 0 0 2]

[0 0 96 576 448 124]

[0 96 1856 2272 1064 224]

[0 576 2272 1552 560 104]

[0 448 1064 560 168 28]

[2 124 224 104 28 4]

(End)

Links

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

Empirical: a(n) = 14576*n^2 - 77924*n + 99292 for n>4.

Example

Some solutions for 3X3
..0..2..0....0..4..0....0..4..3....0..0..0....0..2..1....3..2..0....0..4..5
..1..3..4....2..3..5....6..5..2....1..2..6....0..4..3....4..0..1....3..0..6
..6..5..0....1..6..0....0..0..1....3..4..5....0..5..6....6..5..0....1..2..0

Crossrefs

Row 6 of A186861.

Sequence in context: A378563 A372248 A079013 * A038728 A002520 A337416

Adjacent sequences: A186862 A186863 A186864 * A186866 A186867 A186868

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Status

approved