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

1,2

Links

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

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.

Example

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

Crossrefs

Row 2 is A035006.

Sequence in context: A352672 A188147 A187286 * A021248 A269843 A247127

Adjacent sequences: A187186 A187187 A187188 * A187190 A187191 A187192

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 06 2011

Status

approved