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A187029
Number of 4-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.
1
0, 24, 1344, 7056, 19568, 39348, 66360, 100380, 141408, 189444, 244488, 306540, 375600, 451668, 534744, 624828, 721920, 826020, 937128, 1055244, 1180368, 1312500, 1451640, 1597788, 1750944, 1911108, 2078280, 2252460, 2433648, 2621844
OFFSET
1,2
Row 4 of A187027.
FORMULA
Empirical: a(n) = 3504*n^2 - 18540*n + 24444 for n>5.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^2*(6 + 318*x + 774*x^2 + 602*x^3 + 117*x^4 - 9*x^5 - 56*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)
EXAMPLE
Some solutions for 4 X 4:
..0..0..0..0....2..0..3..4....0..0..0..4....0..0..0..0....0..2..0..0
..0..0..0..1....0..1..0..0....1..2..3..0....2..3..0..0....4..1..3..0
..0..0..3..4....0..0..0..0....0..0..0..0....1..0..0..0....0..0..0..0
..0..0..0..2....0..0..0..0....0..0..0..0....0..4..0..0....0..0..0..0
CROSSREFS
Cf. A187027.
Sequence in context: A374888 A367706 A188807 * A186967 A068294 A003170
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 02 2011
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)