|
%I #12 Sep 03 2016 10:12:04
%S 0,0,0,384,88264,1665344,14497784,80088992,335122320,1142391712,
%T 3358831216,8772323808,20882774744,46000760736,95075730152,
%U 186010966464,347367851808,622687135680,1077266143968,1805545001664,2942598571752
%N Number of 8-turn bishop's tours on an n X n board summed over all starting positions
%C Row 8 of A188777
%F From _Vaclav Kotesovec_, Sep 01 2012: (Start)
%F Empirical: Recurrence: a(n) = a(n-17) - 5*a(n-16) + 4*a(n-15) + 20*a(n-14) - 40*a(n-13) - 16*a(n-12) + 100*a(n-11) - 44*a(n-10) - 110*a(n-9) + 110*a(n-8) + 44*a(n-7) - 100*a(n-6) + 16*a(n-5) + 40*a(n-4) - 20*a(n-3) - 4*a(n-2) + 5*a(n-1)
%F Empirical: G.f.: 8*x^4*(48 + 10841*x + 164036*x^2 + 980511*x^3 + 2981932*x^4 + 5786766*x^5 + 6924788*x^6 + 5849090*x^7 + 3007252*x^8 + 1111577*x^9 + 201048*x^10 + 23391*x^11)/((1-x)^10*(1+x)^6)
%F Empirical: a(n) = -31395/16 + 31519*n/2 - 50452903*n^2/1260 + 13521503*n^3/270 - 4517641*n^4/120 + 224087*n^5/12 - 93658*n^6/15 + 60857*n^7/45 - 428119*n^8/2520 + 503*n^9/54 + (-1)^n*(31395/16 - 55203*n/10 + 20473*n^2/4 - 4275*n^3/2 + 3349*n^4/8 - 629*n^5/20)
%F (End)
%e Some solutions for 4X4
%e ..0..3..0..8....4..0..7..0....4..0..8..0....0..5..0..1....0..8..0..1
%e ..6..0..2..0....0..6..0..1....0..2..0..7....6..0..3..0....5..0..3..0
%e ..0..7..0..4....8..0..3..0....1..0..5..0....0..8..0..4....0..4..0..7
%e ..1..0..5..0....0..2..0..5....0..6..0..3....2..0..7..0....2..0..6..0
%K nonn
%O 1,4
%A _R. H. Hardin_ Apr 10 2011
| 