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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 9
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 (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
.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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 14 2011
STATUS
approved

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Last modified June 15 11:51 EDT 2024. Contains 373407 sequences. (Running on oeis4.)