

A187175


Number of 5step lefthanded knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.


1



0, 0, 0, 0, 16, 136, 456, 1024, 1804, 2784, 3964, 5344, 6924, 8704, 10684, 12864, 15244, 17824, 20604, 23584, 26764, 30144, 33724, 37504, 41484, 45664, 50044, 54624, 59404, 64384, 69564, 74944, 80524, 86304, 92284, 98464, 104844, 111424, 118204, 125184
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OFFSET

1,5


COMMENTS

Row 5 of A187172.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..50


FORMULA

Empirical: a(n) = 100*n^2  920*n + 1984 for n>7.
G.f.: 4*x^5*(2  x)*(2 + 12*x + 18*x^2 + 15*x^3 + 3*x^4) / (1  x)^3 (conjectured).  Colin Barker, Apr 22 2018


EXAMPLE

Some solutions for 5 X 5:
..1..0..0..0..0....0..0..3..0..0....0..0..0..0..1....0..0..0..0..5
..0..0..0..3..0....2..0..0..0..0....0..0..2..0..0....0..0..4..0..0
..0..2..0..0..0....0..0..0..4..0....3..0..0..0..0....1..0..0..0..0
..0..0..0..0..4....0..1..0..0..0....0..0..0..5..0....0..0..0..3..0
..0..0..5..0..0....0..0..0..0..5....0..4..0..0..0....0..2..0..0..0


CROSSREFS

Cf. A187172.
Sequence in context: A253303 A139616 A304506 * A302319 A303013 A059421
Adjacent sequences: A187172 A187173 A187174 * A187176 A187177 A187178


KEYWORD

nonn


AUTHOR

R. H. Hardin, Mar 06 2011


STATUS

approved



