|
| |
|
|
A187189
|
|
T(n,k) = Number of n-turn rook's tours on a k X k board summed over all starting positions.
|
|
7
|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
