A187189 T(n,k) = Number of n-turn 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, 96, 108, 8, 0, 36, 200, 480, 288, 0, 0, 49, 360, 1400, 2208, 720, 0, 0, 64, 588, 3240, 9200, 9792, 1440, 0, 0, 81, 896, 6468, 27720, 58800, 40896, 2304, 0, 0, 100, 1296, 11648, 68208, 231840, 364800, 156672, 2664, 0, 0, 121, 1800

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn
• tabl

Examples

			Table starts
.1.4....9......16.......25........36........49........64.......81.....100
.0.8...36......96......200.......360.......588.......896.....1296....1800
.0.8..108.....480.....1400......3240......6468.....11648....19440...30600
.0.8..288....2208.....9200.....27720.....68208....146048...282528..505800
.0.0..720....9792....58800....231840....705600...1800960..4046112.8251200
.0.0.1440...40896...364800...1902240...7197120..21960960.57407616
.0.0.2304..156672..2169600..15220800..72182880.264520704
.0.0.2664..551232.12319200.118332000.709921800
.0.0.1512.1760256.66746400.893246400
.0.0....0.5013504
Some n=3 solutions for 3 X 3
..0..0..1....0..0..3....3..2..0....1..0..0....0..0..1....0..0..0....0..0..3
..0..0..0....0..0..2....0..1..0....0..0..0....0..3..2....0..0..0....0..0..1
..0..3..2....0..0..1....0..0..0....2..0..3....0..0..0....1..3..2....0..0..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..100

Crossrefs

Row 2 is A035006.

Formula

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

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

Empirical: T(3,k) = 4*k^4 - 10*k^3 + 6*k^2.

Empirical: T(4,k) = 8*k^5 - 34*k^4 + 48*k^3 - 22*k^2.

Empirical: T(5,k) = 16*k^6 - 98*k^5 + 228*k^4 - 238*k^3 + 92*k^2.

Empirical: T(6,k) = 32*k^7 - 258*k^6 + 846*k^5 - 1426*k^4 + 1234*k^3 - 428*k^2.

Empirical: T(7,k) = 64*n^8 - 642*n^7 + 2718*n^6 - 6346*n^5 + 8770*n^4 - 6788*n^3 + 2224*n^2.

Empirical: T(8,k) = 128*k^9 - 1538*k^8 + 7956*k^7 - 23556*k^6 + 44586*k^5 - 55218*k^4 + 40894*k^3 - 13252*k^2.