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A187173 Number of 3-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 0,0,0,16,60,128,220,336,476,640,828,1040,1276,1536,1820,2128,2460,

%T 2816,3196,3600,4028,4480,4956,5456,5980,6528,7100,7696,8316,8960,

%U 9628,10320,11036,11776,12540,13328,14140,14976,15836,16720,17628,18560,19516,20496

%N Number of 3-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 3 of A187172.

%H R. H. Hardin, <a href="/A187173/b187173.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 12*n^2 - 64*n + 80 for n>3.

%F G.f.: 4*x^4*(4 - x)*(1 + x) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018

%e Some solutions for 4 X 4:

%e ..0..0..2..0....0..0..1..0....0..0..0..0....0..0..0..0....0..0..1..0

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

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

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

%Y Cf. A187172.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 06 2011

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Last modified January 20 07:59 EST 2020. Contains 331081 sequences. (Running on oeis4.)