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 A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions. 1

%I

%S 0,0,20,330,1224,2726,4807,7458,10679,14470,18831,23762,29263,35334,

%T 41975,49186,56967,65318,74239,83730,93791,104422,115623,127394,

%U 139735,152646,166127,180178,194799,209990,225751,242082,258983,276454,294495

%N Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%C Row 7 of A187507.

%H R. H. Hardin, <a href="/A187512/b187512.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 285*n^2 - 1624*n + 2210 for n>5.

%F Conjectures from _Colin Barker_, Apr 24 2018: (Start)

%F G.f.: x^3*(1 + x)*(20 + 250*x + 44*x^2 - 20*x^3 - 9*x^4) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....1..2..0..0....0..5..3..1....0..0..1..2....4..5..6..0

%e ..0..7..0..0....0..3..4..0....0..6..4..2....0..7..5..3....2..3..7..0

%e ..1..5..6..0....0..7..5..0....0..7..0..0....0..0..6..4....0..1..0..0

%e ..2..3..4..0....0..0..6..0....0..0..0..0....0..0..0..0....0..0..0..0

%Y Cf. A187507.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 10 2011

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)