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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. 1

%I

%S 0,0,12,390,1910,4880,9250,14969,22026,30421,40154,51225,63634,77381,

%T 92466,108889,126650,145749,166186,187961,211074,235525,261314,288441,

%U 316906,346709,377850,410329,444146,479301,515794,553625,592794,633301

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

%C Row 8 of A187507.

%H R. H. Hardin, <a href="/A187513/b187513.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 669*n^2 - 4316*n + 6681 for n>6.

%F 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 Some solutions for 4X4

%e ..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0

%e ..4..5..6..0....3..4..5..6....5..0..0..0....2..6..7..8....6..4..2..0

%e ..0..3..1..0....0..2..0..7....6..4..2..0....3..4..5..0....7..8..3..1

%e ..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....0..0..0..0

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 10 2011

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)