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

1,2

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

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

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

Adjacent sequences: A187293 A187294 A187295 * A187297 A187298 A187299

Keyword

nonn,tabl

Author

R. H. Hardin Mar 08 2011

Status

approved