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A188780 Number of 5-turn bishop's tours on an n X n board summed over all starting positions.

%I A188780 #13 Jul 22 2025 11:23:09
%S A188780 0,0,8,584,5464,26360,91120,252720,603696,1288592,2525400,4620728,
%T A188780 7998984,13219528,21014336,32306400,48256608,70282656,100115880,
%U A188780 139819944,191858360,259112216,344959120,453289232,588596368,755991600
%N A188780 Number of 5-turn bishop's tours on an n X n board summed over all starting positions.
%C A188780 Row 5 of A188777
%H A188780 R. H. Hardin, <a href="/A188780/b188780.txt">Table of n, a(n) for n = 1..42</a>
%F A188780 Empirical: a(n) = 4*a(n-1) -3*a(n-2) -8*a(n-3) +14*a(n-4) -14*a(n-6) +8*a(n-7) +3*a(n-8) -4*a(n-9) +a(n-10)
%F A188780 Contribution from _Vaclav Kotesovec_, Sep 01 2012: (Start)
%F A188780 Empirical: G.f.: 8*x^3*(1 + 69*x + 394*x^2 + 790*x^3 + 829*x^4 + 357*x^5 + 84*x^6)/((1-x)^7*(1+x)^3)
%F A188780 Empirical: a(n) = 51/4 - 913*n/10 + 69203*n^2/360 - 602*n^3/3 + 1007*n^4/9 - 473*n^5/15 + 631*n^6/180 + (-1)^n*(-51/4 + 25*n/2 - 23*n^2/8)
%F A188780 (End)
%e A188780 Some solutions for 4X4
%e A188780 ..0..5..0..0....0..5..0..0....0..5..0..0....0..0..2..0....0..4..0..0
%e A188780 ..1..0..4..0....0..0..1..0....0..0..3..0....0..5..0..3....0..0..3..0
%e A188780 ..0..3..0..0....0..2..0..4....0..2..0..4....1..0..4..0....0..2..0..5
%e A188780 ..0..0..2..0....0..0..3..0....1..0..0..0....0..0..0..0....0..0..1..0
%K A188780 nonn
%O A188780 1,3
%A A188780 _R. H. Hardin_ Apr 10 2011