|
%I #6 Mar 31 2012 12:36:13
%S 1,4,0,9,4,0,16,20,0,0,25,56,28,0,0,36,120,152,24,0,0,49,220,488,328,
%T 8,0,0,64,364,1192,1720,584,0,0,0,81,560,2468,5816,5464,840,0,0,0,100,
%U 816,4560,15424,26360,15824,784,0,0,0,121,1140,7760,34736,91120,112680,40496
%N T(n,k)=Number of n-turn bishop's tours on a kXk board summed over all starting positions
%C Table starts
%C .1.4..9..16.....25......36.......49.......64.......81......100.....121....144
%C .0.4.20..56....120.....220......364......560......816.....1140....1540...2024
%C .0.0.28.152....488....1192.....2468.....4560.....7760....12400...18860..27560
%C .0.0.24.328...1720....5816....15424....34736....69776...128528..221448.361528
%C .0.0..8.584...5464...26360....91120...252720...603696..1288592.2525400
%C .0.0..0.840..15824..112680...516160..1778608..5082912.12622640
%C .0.0..0.784..40496..451104..2803552.12139552.41792672
%C .0.0..0.384..88264.1665344.14497784.80088992
%C .0.0..0...0.159704.5607456
%C .0.0..0...0.229296
%H R. H. Hardin, <a href="/A188777/b188777.txt">Table of n, a(n) for n = 1..113</a>
%F Empirical: T(1,k) = k^2
%F Empirical: T(2,k) = (4/3)*k^3 - 2*k^2 + (2/3)*k
%F Empirical: T(3,k) = 4*T(3,k-1)-5*T(3,k-2)+5*T(3,k-4)-4*T(3,k-5)+T(3,k-6)
%F Empirical: T(4,k) = 4*T(4,k-1)-4*T(4,k-2)-4*T(4,k-3)+10*T(4,k-4)-4*T(4,k-5)-4*T(4,k-6)+4*T(4,k-7)-T(4,k-8)
%F Empirical: T(5,k) = 4*T(5,k-1)-3*T(5,k-2)-8*T(5,k-3)+14*T(5,k-4)-14*T(5,k-6)+8*T(5,k-7)+3*T(5,k-8)-4*T(5,k-9)+T(5,k-10)
%F Empirical: T(6,k) = 4*T(6,k-1)-2*T(6,k-2)-12*T(6,k-3)+17*T(6,k-4)+8*T(6,k-5)-28*T(6,k-6)+8*T(6,k-7)+17*T(6,k-8)-12*T(6,k-9)-2*T(6,k-10)+4*T(6,k-11)-T(6,k-12)
%e Some n=4 solutions for 4X4
%e ..0..0..0..0....0..4..0..1....0..0..0..4....3..0..0..0....0..1..0..0
%e ..0..3..0..0....0..0..3..0....0..0..0..0....0..2..0..0....4..0..2..0
%e ..2..0..4..0....0..2..0..0....0..3..0..1....0..0..4..0....0..3..0..0
%e ..0..1..0..0....0..0..0..0....0..0..2..0....0..0..0..1....0..0..0..0
%Y Row 2 is A002492(n-1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Apr 10 2011
|
