

A187173


Number of 3step 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, 16, 60, 128, 220, 336, 476, 640, 828, 1040, 1276, 1536, 1820, 2128, 2460, 2816, 3196, 3600, 4028, 4480, 4956, 5456, 5980, 6528, 7100, 7696, 8316, 8960, 9628, 10320, 11036, 11776, 12540, 13328, 14140, 14976, 15836, 16720, 17628, 18560, 19516, 20496
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OFFSET

1,4


COMMENTS

Row 3 of A187172.


LINKS

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


FORMULA

Empirical: a(n) = 12*n^2  64*n + 80 for n>3.
G.f.: 4*x^4*(4  x)*(1 + x) / (1  x)^3 (conjectured).  Colin Barker, Apr 22 2018


EXAMPLE

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


CROSSREFS

Cf. A187172.
Sequence in context: A027117 A292537 A258730 * A296958 A258731 A316125
Adjacent sequences: A187170 A187171 A187172 * A187174 A187175 A187176


KEYWORD

nonn


AUTHOR

R. H. Hardin, Mar 06 2011


STATUS

approved



