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.

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

Author

R. H. Hardin Mar 08 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..201

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