A187606 T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on a kXk board summed over all starting positions

1, 4, 0, 9, 1, 0, 16, 9, 0, 0, 25, 25, 9, 0, 0, 36, 49, 36, 0, 0, 0, 49, 81, 100, 28, 0, 0, 0, 64, 121, 196, 144, 8, 0, 0, 0, 81, 169, 324, 340, 130, 0, 0, 0, 0, 100, 225, 484, 675, 500, 96, 0, 0, 0, 0, 121, 289, 676, 1120, 1274, 711, 48, 0, 0, 0, 0, 144, 361, 900, 1675, 2372, 2083

Offset

1,2

Comments

Table starts

.1.4.9.16..25..36...49....64....81....100....121....144.....169.....196.....225

.0.1.9.25..49..81..121...169...225....289....361....441.....529.....625.....729

.0.0.9.36.100.196..324...484...676....900...1156...1444....1764....2116....2500

.0.0.0.28.144.340..675..1120..1675...2340...3115...4000....4995....6100....7315

.0.0.0..8.130.500.1274..2372..3953...5920...8273..11012...14137...17648...21545

.0.0.0..0..96.711.2083..4758..8979..14434..21526..29978...39790...50962...63494

.0.0.0..0..48.616.2936..8530.17611..32086..51955..76258..105978..140386..179482

.0.0.0..0...0.474.3780.12946.32869..68308.117760.187311..275272..379035..500919

.0.0.0..0...0.362.4168.19356.60155.132926.258163.445800..686062..997020.1370430

.0.0.0..0...0.124.3932.27316.92836.246888.539994.978245.1634722.2520047.3595001

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical: T(1,k) = k^2

Empirical: T(2,k) = 4*k^2 - 12*k + 9 for k>1

Empirical: T(3,k) = 16*k^2 - 80*k + 100 for k>3

Empirical: T(4,k) = 55*k^2 - 380*k + 640 for k>5

Empirical: T(5,k) = 193*k^2 - 1700*k + 3620 for k>7

Empirical: T(6,k) = 680*k^2 - 7188*k + 18314 for k>9

Empirical: T(7,k) = 2344*k^2 - 28880*k + 85282 for k>11

Empirical: T(8,k) = 8156*k^2 - 114640*k + 385419 for k>13

Example

Some n=5 solutions for 5X5
..5..0..0..0..0....0..0..2..0..0....0..0..0..5..0....5..0..0..0..0
..0..4..0..0..1....0..0..0..1..0....0..0..0..0..4....0..4..0..0..0
..0..0..3..0..0....0..0..0..0..3....0..0..3..0..0....0..0..3..0..0
..0..0..0..2..0....0..0..5..0..0....0..0..0..2..0....2..0..0..0..0
..0..0..0..0..0....0..0..0..4..0....0..0..0..0..1....0..1..0..0..0

Crossrefs

Row 2 is A016754(n-2)

Sequence in context: A364101 A081148 A306954 * A138478 A213472 A305742

Adjacent sequences: A187603 A187604 A187605 * A187607 A187608 A187609

Keyword

nonn,tabl

Author

R. H. Hardin Mar 11 2011

Status

approved