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%I #9 Apr 18 2022 17:48:21
%S 1,4,0,9,4,0,16,16,0,0,25,36,20,0,0,36,64,64,8,0,0,49,100,132,92,0,0,
%T 0,64,144,224,248,72,0,0,0,81,196,340,476,388,56,0,0,0,100,256,480,
%U 776,904,456,16,0,0,0,121,324,644,1148,1620,1588,544,0,0,0,0,144,400,832,1592
%N T(n,k)=Number of n-step one space at a time bishop's tours on a kXk board summed over all starting positions
%H R. H. Hardin, <a href="/A187155/b187155.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical: T(1,k) = k^2
%F Empirical: T(2,k) = 4*k^2 - 8*k + 4
%F Empirical: T(3,k) = 12*k^2 - 40*k + 32 for k>1
%F Empirical: T(4,k) = 36*k^2 - 168*k + 188 for k>2
%F Empirical: T(5,k) = 100*k^2 - 584*k + 808 for k>3
%F Empirical: T(6,k) = 284*k^2 - 1992*k + 3316 for k>4
%F Empirical: T(7,k) = 780*k^2 - 6296*k + 12024 for k>5
%F Empirical: T(8,k) = 2172*k^2 - 19816*k + 42860 for k>6
%e Table starts
%e .1.4..9.16..25...36....49....64.....81....100....121....144....169.....196
%e .0.4.16.36..64..100...144...196....256....324....400....484....576.....676
%e .0.0.20.64.132..224...340...480....644....832...1044...1280...1540....1824
%e .0.0..8.92.248..476...776..1148...1592...2108...2696...3356...4088....4892
%e .0.0..0.72.388..904..1620..2536...3652...4968...6484...8200..10116...12232
%e .0.0..0.56.456.1588..3288..5556...8392..11796..15768..20308..25416...31092
%e .0.0..0.16.544.2328..6172.11576..18540..27064..37148..48792..61996...76760
%e .0.0..0..0.472.3504.10576.23340..40448..61900..87696.117836.152320..191148
%e .0.0..0..0.392.4216.17696.43136..83844.136384.200756.276960.364996..464864
%e .0.0..0..0.168.5472.26912.80392.168104.296708.457848.651524.877736.1136484
%e Some n=4 solutions for 4X4
%e ..0..0..0..1....0..0..1..0....4..0..0..0....0..4..0..0....0..0..1..0
%e ..0..0..2..0....0..2..0..0....0..3..0..0....3..0..1..0....0..2..0..4
%e ..0..3..0..0....0..0..3..0....0..0..2..0....0..2..0..0....0..0..3..0
%e ..0..0..4..0....0..4..0..0....0..0..0..1....0..0..0..0....0..0..0..0
%Y Row 2 is A016742(n-1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 06 2011
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