A187377 T(n,k)=Number of n-step S, NW and NE-moving king's tours on a kXk board summed over all starting positions.

1, 4, 0, 9, 4, 0, 16, 14, 4, 0, 25, 30, 25, 4, 0, 36, 52, 64, 40, 0, 0, 49, 80, 121, 132, 40, 0, 0, 64, 114, 196, 278, 188, 24, 0, 0, 81, 154, 289, 478, 487, 264, 18, 0, 0, 100, 200, 400, 732, 924, 832, 324, 0, 0, 0, 121, 252, 529, 1040, 1499, 1810, 1418, 404, 0, 0, 0, 144, 310, 676

Offset: 1

Author

R. H. Hardin Mar 09 2011

Keywords

• nonn
• tabl

Comments

Table starts

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

.0.4.14..30...52....80...114...154....200....252....310....374....444....520

.0.4.25..64..121...196...289...400....529....676....841...1024...1225...1444

.0.4.40.132..278...478...732..1040...1402...1818...2288...2812...3390...4022

.0.0.40.188..487...924..1499..2212...3063...4052...5179...6444...7847...9388

.0.0.24.264..832..1810..3154..4864...6940...9382..12190..15364..18904..22810

.0.0.18.324.1418..3448..6581.10688..15769..21824..28853..36856..45833..55784

.0.0..0.404.2140..6380.13220.22996..35366..50330..67888..88040.110786.136126

.0.0..0.340.3060.10320.24892.46412..75567.111492.154187.203652.259887.322892

.0.0..0.280.3792.17052.44464.92628.159328.245946.350386.472648.612732.770638

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Row 2 is A049451(n-1)

Row 3 is A016790(n-2)

Formula

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

Empirical: T(2,k) = 3*k^2 - 5*k + 2

Empirical: T(3,k) = 9*k^2 - 24*k + 16 for k>1

Empirical: T(4,k) = 27*k^2 - 97*k + 88 for k>2

Empirical: T(5,k) = 69*k^2 - 322*k + 372 for k>3

Empirical: T(6,k) = 183*k^2 - 1035*k + 1432 for k>4

Empirical: T(7,k) = 487*k^2 - 3198*k + 5104 for k>5

Empirical: T(8,k) = 1297*k^2 - 9679*k + 17420 for k>6

Empirical: T(9,k) = 3385*k^2 - 28390*k + 56892 for k>7

Empirical: T(10,k) = 8911*k^2 - 82691*k + 181756 for k>8