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

1,2

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

Links

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

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

Example

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

Crossrefs

Row 2 is A181890(n-2)

Sequence in context: A035102 A242015 A187507 * A215499 A190262 A187586

Adjacent sequences: A187854 A187855 A187856 * A187858 A187859 A187860

Keyword

nonn,tabl

Author

R. H. Hardin Mar 14 2011

Status

approved