A187286 T(n,k) = number of n-step one or two space at a time rook's tours on a k X k board summed over all starting positions.

1, 4, 0, 9, 8, 0, 16, 36, 8, 0, 25, 80, 108, 8, 0, 36, 140, 328, 288, 0, 0, 49, 216, 672, 1256, 720, 0, 0, 64, 308, 1128, 3084, 4576, 1440, 0, 0, 81, 416, 1696, 5712, 13640, 15424, 2304, 0, 0, 100, 540, 2376, 9120, 28224, 57288, 47648, 2664, 0, 0, 121, 680, 3168

Offset: 1

Author

R. H. Hardin, Mar 08 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1.4....9.....16.......25.......36.......49.......64......81....100....121

.0.8...36.....80......140......216......308......416.....540....680....836

.0.8..108....328......672.....1128.....1696.....2376....3168...4072...5088

.0.8..288...1256.....3084.....5712.....9120....13288...18216..23904..30352

.0.0..720...4576....13640....28224....48232....73408..103692.139056.179500

.0.0.1440..15424....57288...134408...248208...397152..580328.797160

.0.0.2304..47648...228512...616752..1241936..2102944.3192912

.0.0.2664.134944...866888..2732016..6049424.10906120

.0.0.1512.345120..3123680.11693984.28716816

.0.0....0.789696.10664384.48391584

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..117

Formula

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

Empirical: T(2,k) = 8*k^2 - 12*k for k>1

Empirical: T(3,k) = 56*k^2 - 160*k + 72 for k>3

Empirical: T(4,k) = 380*k^2 - 1532*k + 1224 for k>5

Empirical: T(5,k) = 2540*k^2 - 12896*k + 14016 for k>7

Empirical: T(6,k) = 16752*k^2 - 101420*k + 136160 for k>9

Empirical: T(7,k) = 109360*k^2 - 763776*k + 1206864 for k>11

Empirical: T(8,k) = 708492*k^2 - 5580668*k + 10074432 for k>13

Empirical: T(9,k) = 4562676*k^2 - 39873424*k + 80572112 for k>15

Empirical: T(10,k) = 29244672*k^2 - 280021012*k + 623972304 for k>17