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A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187513 #12 Nov 27 2017 12:49:18
%S A187513 0,0,12,390,1910,4880,9250,14969,22026,30421,40154,51225,63634,77381,
%T A187513 92466,108889,126650,145749,166186,187961,211074,235525,261314,288441,
%U A187513 316906,346709,377850,410329,444146,479301,515794,553625,592794,633301
%N A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%C A187513 Row 8 of A187507.
%H A187513 R. H. Hardin, <a href="/A187513/b187513.txt">Table of n, a(n) for n = 1..50</a>
%F A187513 Empirical: a(n) = 669*n^2 - 4316*n + 6681 for n>6.
%F A187513 Empirical g.f.: x^3*(12 + 354*x + 776*x^2 + 308*x^3 - 50*x^4 - 51*x^5 - 11*x^6) / (1 - x)^3. - _Colin Barker_, Nov 27 2017
%e A187513 Some solutions for 4X4
%e A187513 ..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0
%e A187513 ..4..5..6..0....3..4..5..6....5..0..0..0....2..6..7..8....6..4..2..0
%e A187513 ..0..3..1..0....0..2..0..7....6..4..2..0....3..4..5..0....7..8..3..1
%e A187513 ..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....0..0..0..0
%K A187513 nonn
%O A187513 1,3
%A A187513 _R. H. Hardin_, Mar 10 2011