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A187586 T(n,k)=Number of n-step E, S, NW and NE-moving king's tours on a kXk board summed over all starting positions 8
1, 4, 0, 9, 6, 0, 16, 20, 8, 0, 25, 42, 48, 5, 0, 36, 72, 120, 84, 0, 0, 49, 110, 224, 286, 106, 0, 0, 64, 156, 360, 604, 578, 104, 0, 0, 81, 210, 528, 1038, 1484, 1069, 78, 0, 0, 100, 272, 728, 1588, 2794, 3514, 1708, 34, 0, 0, 121, 342, 960, 2254, 4508, 7480, 7666, 2309, 13 (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

.0.6..20...42....72....110....156.....210.....272.....342.....420.....506

.0.8..48..120...224....360....528.....728.....960....1224....1520....1848

.0.5..84..286...604...1038...1588....2254....3036....3934....4948....6078

.0.0.106..578..1484...2794...4508....6626....9148...12074...15404...19138

.0.0.104.1069..3514...7480..12874...19696...27946...37624...48730...61264

.0.0..78.1708..7666..19104..35832...57592...84384..116208..153064..194952

.0.0..34.2309.15056..45718..95776..164135..250132..353767..475040..613951

.0.0..13.2792.27252.103108.246792..458018..732810.1069534.1468190.1928778

.0.0...0.3108.45960.219432.609070.1243461.2111652.3201436.4508924

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

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

Empirical: T(2,k) = 4*k^2 - 6*k + 2

Empirical: T(3,k) = 16*k^2 - 40*k + 24

Empirical: T(4,k) = 58*k^2 - 204*k + 174 for k>2

Empirical: T(5,k) = 202*k^2 - 912*k + 994 for k>3

Empirical: T(6,k) = 714*k^2 - 3888*k + 5104 for k>4

Empirical: T(7,k) = 2516*k^2 - 15980*k + 24408 for k>5

Empirical: T(8,k) = 8819*k^2 - 63926*k + 111127 for k>6

Empirical: T(9,k) = 30966*k^2 - 251630*k + 489234 for k>7

Empirical: T(10,k) = 108852*k^2 - 978404*k + 2100276 for k>8

EXAMPLE

Some k=4 solutions for 4X4

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

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

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

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

CROSSREFS

Row 2 is A002943(n-1)

Row 3 is A152750(n-1)

Sequence in context: A187857 A215499 A190262 * A198866 A269720 A245638

Adjacent sequences:  A187583 A187584 A187585 * A187587 A187588 A187589

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 11 2011

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.