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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 8
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 (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

.0.4.14..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

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Last modified October 21 04:00 EDT 2021. Contains 348141 sequences. (Running on oeis4.)