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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.
10
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
1,2
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
LINKS
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
EXAMPLE
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
CROSSREFS
Sequence in context: A357017 A352672 A188147 * A187189 A021248 A269843
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 08 2011
STATUS
approved