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A187850 T(n,k)=Number of n-step king-knight's tours (piece capable of both kinds of moves) on a kXk board summed over all starting positions 7
1, 4, 0, 9, 12, 0, 16, 56, 24, 0, 25, 132, 304, 24, 0, 36, 240, 1056, 1400, 0, 0, 49, 380, 2312, 7620, 5328, 0, 0, 64, 552, 4048, 20952, 49776, 16032, 0, 0, 81, 756, 6264, 41652, 177040, 292776, 35328, 0, 0, 100, 992, 8960, 69456, 408048, 1400168, 1533064, 49536 (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

.0.12....56......132.......240.......380.......552.......756......992....1260

.0.24...304.....1056......2312......4048......6264......8960....12136...15792

.0.24..1400.....7620.....20952.....41652.....69456....104268...146088..194916

.0..0..5328....49776....177040....408048....744696...1183632..1723120.2362864

.0..0.16032...292776...1400168...3807828...7700944..13082348.19910456

.0..0.35328..1533064..10353632..33908456..76860784.140714528

.0..0.49536..7067600..71450504.288493336.741624088

.0..0.32256.28260592.458862208

.0..0.....0.96217616

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..99

FORMULA

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

Empirical: T(2,k) = 16*k^2 - 36*k + 20

Empirical: T(3,k) = 240*k^2 - 904*k + 832 for k>3

Empirical: T(4,k) = 3504*k^2 - 17748*k + 21996 for k>5

Empirical: T(5,k) = 50128*k^2 - 312688*k + 476944 for k>7

Empirical: T(6,k) = 706880*k^2 - 5180252*k + 9274644 for k>9

Empirical: T(7,k) = 9862808*k^2 - 82444808*k + 168212080 for k>11

Empirical: T(8,k) = 136526552*k^2 - 1275583564*k + 2906368876 for k>13

EXAMPLE

Some n=4 solutions for 4X4

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

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

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

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

CROSSREFS

Row 2 is A104188(n-1)

Sequence in context: A195056 A186861 A187027 * A186965 A330386 A098487

Adjacent sequences:  A187847 A187848 A187849 * A187851 A187852 A187853

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 14 2011

STATUS

approved

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Last modified October 3 13:22 EDT 2022. Contains 357237 sequences. (Running on oeis4.)