A187383 Number of 9-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 0, 340, 3060, 10320, 24892, 46412, 75567, 111492, 154187, 203652, 259887, 322892, 392667, 469212, 552527, 642612, 739467, 843092, 953487, 1070652, 1194587, 1325292, 1462767, 1607012, 1758027, 1915812, 2080367, 2251692, 2429787, 2614652

Offset: 1

Author

R. H. Hardin, Mar 09 2011

Keywords

• nonn

Comments

Row 9 of A187377.

Links

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

Crossrefs

Cf. A187377.

Formula

Empirical: a(n) = 3385*n^2 - 28390*n + 56892 for n>7.

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

G.f.: x^4*(340 + 2040*x + 2160*x^2 + 2772*x^3 - 364*x^4 + 687*x^5 - 865*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)