A187857 T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on a kXk board summed over all starting positions.

1, 4, 0, 9, 5, 0, 16, 27, 2, 0, 25, 65, 81, 0, 0, 36, 119, 254, 216, 0, 0, 49, 189, 578, 968, 486, 0, 0, 64, 275, 1030, 2754, 3320, 846, 0, 0, 81, 377, 1610, 5428, 11986, 9932, 1206, 0, 0, 100, 495, 2318, 9237, 26836, 47962, 26584, 1008, 0, 0, 121, 629, 3154, 14040

Offset: 1

Author

R. H. Hardin Mar 14 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1.4....9.....16......25.......36........49.......64.......81.....100.....121

.0.5...27.....65.....119......189.......275......377......495.....629.....779

.0.2...81....254.....578.....1030......1610.....2318.....3154....4118....5210

.0.0..216....968....2754.....5428......9237....14040....19837...26628...34413

.0.0..486...3320...11986....26836.....50378....81124...120051..166504..220483

.0.0..846...9932...47962...126397....262409...452766...707541.1017934.1387600

.0.0.1206..26584..180750...568870...1314428..2456614..4062007.6094090

.0.0.1008..61668..636102..2432312...6343874.12918800.22675997

.0.0..414.124880.2090520..9934272..29607932.65963326

.0.0....0.219008.6387404.38766870.133665550

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..130

Crossrefs

Row 2 is A181890(n-2)

Formula

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

Empirical: T(2,k) = 8*k^2 - 18*k + 9 for k>1

Empirical: T(3,k) = 64*k^2 - 252*k + 238 for k>3

Empirical: T(4,k) = 497*k^2 - 2652*k + 3448 for k>5

Empirical: T(5,k) = 3763*k^2 - 25044*k + 40644 for k>7

Empirical: T(6,k) = 28294*k^2 - 224508*k + 433614 for k>9

Empirical: T(7,k) = 211612*k^2 - 1941340*k + 4328678 for k>11

Empirical: T(8,k) = 1575830*k^2 - 16367550*k + 41250447 for k>13

Empirical: T(9,k) = 11710007*k^2 - 135575032*k + 380311550 for k>15

Empirical: T(10,k) = 86897560*k^2 - 1108193530*k + 3420011978 for k>17