A187377 T(n,k)=Number of n-step S, NW and NE-moving king's tours on a kXk board summed over all starting positions

1, 4, 0, 9, 4, 0, 16, 14, 4, 0, 25, 30, 25, 4, 0, 36, 52, 64, 40, 0, 0, 49, 80, 121, 132, 40, 0, 0, 64, 114, 196, 278, 188, 24, 0, 0, 81, 154, 289, 478, 487, 264, 18, 0, 0, 100, 200, 400, 732, 924, 832, 324, 0, 0, 0, 121, 252, 529, 1040, 1499, 1810, 1418, 404, 0, 0, 0, 144, 310, 676

Offset

1,2

Comments

Table starts

.1.4..9..16...25....36....49....64.....81....100....121....144....169....196

.0.4.14..30...52....80...114...154....200....252....310....374....444....520

.0.4.25..64..121...196...289...400....529....676....841...1024...1225...1444

.0.4.40.132..278...478...732..1040...1402...1818...2288...2812...3390...4022

.0.0.40.188..487...924..1499..2212...3063...4052...5179...6444...7847...9388

.0.0.24.264..832..1810..3154..4864...6940...9382..12190..15364..18904..22810

.0.0.18.324.1418..3448..6581.10688..15769..21824..28853..36856..45833..55784

.0.0..0.404.2140..6380.13220.22996..35366..50330..67888..88040.110786.136126

.0.0..0.340.3060.10320.24892.46412..75567.111492.154187.203652.259887.322892

.0.0..0.280.3792.17052.44464.92628.159328.245946.350386.472648.612732.770638

Links

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

Formula

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

Empirical: T(2,k) = 3*k^2 - 5*k + 2

Empirical: T(3,k) = 9*k^2 - 24*k + 16 for k>1

Empirical: T(4,k) = 27*k^2 - 97*k + 88 for k>2

Empirical: T(5,k) = 69*k^2 - 322*k + 372 for k>3

Empirical: T(6,k) = 183*k^2 - 1035*k + 1432 for k>4

Empirical: T(7,k) = 487*k^2 - 3198*k + 5104 for k>5

Empirical: T(8,k) = 1297*k^2 - 9679*k + 17420 for k>6

Empirical: T(9,k) = 3385*k^2 - 28390*k + 56892 for k>7

Empirical: T(10,k) = 8911*k^2 - 82691*k + 181756 for k>8

Example

Some n=4 solutions for 4X4
..0..4..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....0..0..0..0....2..0..0..0....0..0..0..0....0..0..1..0
..0..2..0..0....0..0..3..1....3..0..0..0....4..2..0..0....0..0..2..4
..0..0..1..0....0..0..4..2....4..0..0..0....0..3..1..0....0..0..3..0

Crossrefs

Row 2 is A049451(n-1)

Row 3 is A016790(n-2)

Sequence in context: A133844 A198238 A344716 * A187155 A187296 A187046

Adjacent sequences: A187374 A187375 A187376 * A187378 A187379 A187380

Keyword

nonn,tabl

Author

R. H. Hardin Mar 09 2011

Status

approved