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 A187175 Number of 5-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions. 1

%I

%S 0,0,0,0,16,136,456,1024,1804,2784,3964,5344,6924,8704,10684,12864,

%T 15244,17824,20604,23584,26764,30144,33724,37504,41484,45664,50044,

%U 54624,59404,64384,69564,74944,80524,86304,92284,98464,104844,111424,118204,125184

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

%C Row 5 of A187172.

%H R. H. Hardin, <a href="/A187175/b187175.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 100*n^2 - 920*n + 1984 for n>7.

%F 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

%e Some solutions for 5 X 5:

%e ..1..0..0..0..0....0..0..3..0..0....0..0..0..0..1....0..0..0..0..5

%e ..0..0..0..3..0....2..0..0..0..0....0..0..2..0..0....0..0..4..0..0

%e ..0..2..0..0..0....0..0..0..4..0....3..0..0..0..0....1..0..0..0..0

%e ..0..0..0..0..4....0..1..0..0..0....0..0..0..5..0....0..0..0..3..0

%e ..0..0..5..0..0....0..0..0..0..5....0..4..0..0..0....0..2..0..0..0

%Y Cf. A187172.

%K nonn

%O 1,5

%A _R. H. Hardin_, Mar 06 2011

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Last modified May 23 03:15 EDT 2022. Contains 353959 sequences. (Running on oeis4.)