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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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: A022899 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

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Last modified November 20 13:03 EST 2019. Contains 329336 sequences. (Running on oeis4.)