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A187507 T(n,k)=Number of n-step S, E, and NW-moving king's tours on a kXk board summed over all starting positions 9
1, 4, 0, 9, 5, 0, 16, 16, 6, 0, 25, 33, 31, 2, 0, 36, 56, 74, 36, 0, 0, 49, 85, 135, 115, 40, 0, 0, 64, 120, 214, 236, 184, 36, 0, 0, 81, 161, 311, 399, 435, 272, 20, 0, 0, 100, 208, 426, 604, 788, 772, 330, 12, 0, 0, 121, 261, 559, 851, 1243, 1525, 1224, 390, 6, 0, 0, 144, 320, 710 (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

.0.5.16..33...56....85...120...161...208....261....320....385....456....533

.0.6.31..74..135...214...311...426...559....710....879...1066...1271...1494

.0.2.36.115..236...399...604...851..1140...1471...1844...2259...2716...3215

.0.0.40.184..435...788..1243..1800..2459...3220...4083...5048...6115...7284

.0.0.36.272..772..1525..2524..3769..5260...6997...8980..11209..13684..16405

.0.0.20.330.1224..2726..4807..7458.10679..14470..18831..23762..29263..35334

.0.0.12.390.1910..4880..9250.14969.22026..30421..40154..51225..63634..77381

.0.0..6.450.2872..8522.17564.29834.45255..63814..85511.110346.138319.169430

.0.0..0.398.3868.13796.31548.56952.89684.129637.176796.231161.292732.361509

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..290

FORMULA

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

Empirical: T(2,k) = 3*k^2 - 4*k + 1

Empirical: T(3,k) = 9*k^2 - 20*k + 10 for k>1

Empirical: T(4,k) = 21*k^2 - 68*k + 51 for k>2

Empirical: T(5,k) = 51*k^2 - 208*k + 200 for k>3

Empirical: T(6,k) = 123*k^2 - 600*k + 697 for k>4

Empirical: T(7,k) = 285*k^2 - 1624*k + 2210 for k>5

Empirical: T(8,k) = 669*k^2 - 4316*k + 6681 for k>6

Empirical: T(9,k) = 1569*k^2 - 11252*k + 19434 for k>7

Empirical: T(10,k) = 3603*k^2 - 28504*k + 54377 for k>8

EXAMPLE

Some n=4 solutions for 4X4

..0..0..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0

..0..0..0..0....0..0..0..0....2..0..0..0....0..0..0..0....2..3..4..0

..0..4..2..0....0..3..4..0....3..0..0..0....3..1..0..0....0..1..0..0

..0..0..3..1....0..1..2..0....4..0..0..0....4..2..0..0....0..0..0..0

CROSSREFS

Row 2 is A045944(n-1)

Sequence in context: A100074 A035102 A242015 * A187857 A215499 A190262

Adjacent sequences:  A187504 A187505 A187506 * A187508 A187509 A187510

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 10 2011

STATUS

approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)