A187507 T(n,k)=Number of n-step S, E, and NW-moving king's tours on a kXk board summed over all starting positions.

1, 4, 0, 9, 5, 0, 16, 16, 6, 0, 25, 33, 31, 2, 0, 36, 56, 74, 36, 0, 0, 49, 85, 135, 115, 40, 0, 0, 64, 120, 214, 236, 184, 36, 0, 0, 81, 161, 311, 399, 435, 272, 20, 0, 0, 100, 208, 426, 604, 788, 772, 330, 12, 0, 0, 121, 261, 559, 851, 1243, 1525, 1224, 390, 6, 0, 0, 144, 320, 710

Offset: 1

Author

R. H. Hardin Mar 10 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1.4..9..16...25....36....49....64....81....100....121....144....169....196

.0.5.16..33...56....85...120...161...208....261....320....385....456....533

.0.6.31..74..135...214...311...426...559....710....879...1066...1271...1494

.0.2.36.115..236...399...604...851..1140...1471...1844...2259...2716...3215

.0.0.40.184..435...788..1243..1800..2459...3220...4083...5048...6115...7284

.0.0.36.272..772..1525..2524..3769..5260...6997...8980..11209..13684..16405

.0.0.20.330.1224..2726..4807..7458.10679..14470..18831..23762..29263..35334

.0.0.12.390.1910..4880..9250.14969.22026..30421..40154..51225..63634..77381

.0.0..6.450.2872..8522.17564.29834.45255..63814..85511.110346.138319.169430

.0.0..0.398.3868.13796.31548.56952.89684.129637.176796.231161.292732.361509

Examples

			Some n=4 solutions for 4X4
..0..0..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....2..0..0..0....0..0..0..0....2..3..4..0
..0..4..2..0....0..3..4..0....3..0..0..0....3..1..0..0....0..1..0..0
..0..0..3..1....0..1..2..0....4..0..0..0....4..2..0..0....0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..290

Crossrefs

Row 2 is A045944(n-1)

Formula

Empirical: T(1,k) = k^2

Empirical: T(2,k) = 3*k^2 - 4*k + 1

Empirical: T(3,k) = 9*k^2 - 20*k + 10 for k>1

Empirical: T(4,k) = 21*k^2 - 68*k + 51 for k>2

Empirical: T(5,k) = 51*k^2 - 208*k + 200 for k>3

Empirical: T(6,k) = 123*k^2 - 600*k + 697 for k>4

Empirical: T(7,k) = 285*k^2 - 1624*k + 2210 for k>5

Empirical: T(8,k) = 669*k^2 - 4316*k + 6681 for k>6

Empirical: T(9,k) = 1569*k^2 - 11252*k + 19434 for k>7

Empirical: T(10,k) = 3603*k^2 - 28504*k + 54377 for k>8