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A187589 Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 104, 1069, 3514, 7480, 12874, 19696, 27946, 37624, 48730, 61264, 75226, 90616, 107434, 125680, 145354, 166456, 188986, 212944, 238330, 265144, 293386, 323056, 354154, 386680, 420634, 456016, 492826, 531064, 570730, 611824, 654346, 698296 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 6 of A187586.
LINKS
FORMULA
Empirical: a(n) = 714*n^2 - 3888*n + 5104 for n>4.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(104 + 757*x + 619*x^2 + 41*x^3 - 93*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
EXAMPLE
Some solutions for 4 X 4:
..0..0..0..0....0..0..0..6....0..0..0..4....0..1..2..0....0..0..6..0
..0..0..6..0....0..4..5..0....0..2..3..5....0..0..3..0....1..3..4..5
..1..3..4..5....0..1..3..0....0..0..1..6....0..0..4..5....2..0..0..0
..2..0..0..0....0..2..0..0....0..0..0..0....0..0..0..6....0..0..0..0
CROSSREFS
Cf. A187586.
Sequence in context: A230028 A340898 A132434 * A200196 A234219 A223420
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2011
STATUS
approved

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Last modified July 22 10:14 EDT 2024. Contains 374490 sequences. (Running on oeis4.)