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A187296
T(n,k)=Number of n-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on a kXk board summed over all starting positions
10
1, 4, 0, 9, 4, 0, 16, 18, 2, 0, 25, 40, 36, 0, 0, 36, 70, 98, 54, 0, 0, 49, 108, 198, 196, 90, 0, 0, 64, 154, 330, 480, 416, 144, 0, 0, 81, 208, 494, 876, 1208, 884, 108, 0, 0, 100, 270, 690, 1398, 2400, 3006, 1368, 72, 0, 0, 121, 340, 918, 2036, 4092, 6520, 6264, 2028, 54
OFFSET
1,2
COMMENTS
Table starts
.1.4...9...16....25.....36.....49......64......81.....100.....121.....144
.0.4..18...40....70....108....154.....208.....270.....340.....418.....504
.0.2..36...98...198....330....494.....690.....918....1178....1470....1794
.0.0..54..196...480....876...1398....2036....2790....3660....4646....5748
.0.0..90..416..1208...2400...4092....6208....8766...11752...15166...19008
.0.0.144..884..3006...6520..11896...18832...27478...37696...49508...62896
.0.0.108.1368..6264..15596..31172...52256...79634..112568..151266..195512
.0.0..72.2028.12778..37124..81362..145100..231552..338044..465734..613212
.0.0..54.2968.25716..87432.209700..399524..668522.1010572.1430378.1921532
.0.0...0.3096.44824.187924.505878.1044900.1847506.2912204.4254568
LINKS
FORMULA
Empirical: T(1,k) = k^2
Empirical: T(2,k) = 4*k^2 - 6*k for k>1
Empirical: T(3,k) = 16*k^2 - 44*k + 18 for k>3
Empirical: T(4,k) = 58*k^2 - 232*k + 180 for k>5
Empirical: T(5,k) = 214*k^2 - 1080*k + 1152 for k>7
Empirical: T(6,k) = 788*k^2 - 4736*k + 6256 for k>9
Empirical: T(7,k) = 2776*k^2 - 19580*k + 30728 for k>11
Empirical: T(8,k) = 9878*k^2 - 79388*k + 143388 for k>13
Empirical: T(9,k) = 35254*k^2 - 316744*k + 644876 for k>15
Empirical: T(10,k) = 124248*k^2 - 1238146*k + 2807812 for k>17
EXAMPLE
Some n=4 solutions for 4X4
..0..0..0..0....0..0..0..0....4..3..2..0....0..0..0..4....0..1..0..0
..0..0..0..1....3..2..4..0....0..0..1..0....0..2..0..3....0..3..0..4
..0..0..4..3....0..1..0..0....0..0..0..0....0..1..0..0....0..2..0..0
..0..0..0..2....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
CROSSREFS
Sequence in context: A344716 A187377 A187155 * A187046 A188777 A016683
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 08 2011
STATUS
approved