A187161 - OEIS

%I #13 Apr 23 2018 12:36:02

%S 0,0,0,0,472,3504,10576,23340,40448,61900,87696,117836,152320,191148,

%T 234320,281836,333696,389900,450448,515340,584576,658156,736080,

%U 818348,904960,995916,1091216,1190860,1294848,1403180,1515856,1632876,1754240

%N Number of 8-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 8 of A187155.

%H R. H. Hardin, <a href="/A187161/b187161.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 2172*n^2 - 19816*n + 42860 for n>6.

%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)

%F G.f.: 4*x^5*(118 + 522*x + 370*x^2 + 413*x^3 - 337*x^4) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

%F (End)

%e Some solutions for 5 X 5:

%e ..0..0..3..0..0....0..0..7..0..0....0..0..0..0..0....0..2..0..0..0

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

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

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

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

%Y Cf. A187155.

%K nonn

%O 1,5

%A _R. H. Hardin_, Mar 06 2011