A187384 Number of 10-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 0, 280, 3792, 17052, 44464, 92628, 159328, 245946, 350386, 472648, 612732, 770638, 946366, 1139916, 1351288, 1580482, 1827498, 2092336, 2374996, 2675478, 2993782, 3329908, 3683856, 4055626, 4445218, 4852632, 5277868, 5720926, 6181806

Offset: 1

Author

R. H. Hardin, Mar 09 2011

Keywords

• nonn

Comments

Row 10 of A187377.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A187377.

Formula

Empirical: a(n) = 8911*n^2 - 82691*n + 181756 for n>8.

Conjectures from Colin Barker, Apr 24 2018: (Start)

G.f.: 2*x^4*(140 + 1476*x + 3258*x^2 + 2202*x^3 + 3300*x^4 - 1108*x^5 + 691*x^6 - 1048*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)