login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 16:12 EST 2019. Contains 329753 sequences. (Running on oeis4.)