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A187174 Number of 4-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 0,0,0,8,48,176,384,664,1016,1440,1936,2504,3144,3856,4640,5496,6424,

%T 7424,8496,9640,10856,12144,13504,14936,16440,18016,19664,21384,23176,

%U 25040,26976,28984,31064,33216,35440,37736,40104,42544,45056,47640,50296

%N Number of 4-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 4 of A187172.

%H R. H. Hardin, <a href="/A187174/b187174.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 36*n^2 - 260*n + 440 for n>5.

%F G.f.: 8*x^4*(1 + 3*x + 7*x^2 - x^3 - x^4) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018

%e Some solutions for 4 X 4:

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

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

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

%e ..0..3..0..0....0..1..0..0....0..2..0..0....0..4..0..0....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 February 19 16:24 EST 2020. Contains 332045 sequences. (Running on oeis4.)