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%I #5 Nov 10 2015 12:42:52
%S 49,475,569,3588,18995,4020,33265,474101,437533,38769,292865,14115520,
%T 30745811,13341380,355145,2600010,452888405,2977192536,3002676432,
%U 414860767,3191484,23355021,14143461755
%N T(n,k)=Number of (n+2)X(k+2) arrays of permutations of 0..(n+2)*(k+2)-1 with each element moved 0 or 1 knight moves and equal numbers of elements advancing and retreating in the array numbered in row major order.
%C Table starts
%C ......49.......475.......3588......33265....292865.....2600010.23355021
%C .....569.....18995.....474101...14115520.452888405.14143461755
%C ....4020....437533...30745811.2977192536
%C ...38769..13341380.3002676432
%C ..355145.414860767
%C .3191484
%e Some solutions for n=2 k=4
%e ..0..1.13.16.15..5....0..1.15.14.17..5....0..1.10..3..4.16....0..1.10.16..8..5
%e ..6..7..8.20.23.11....6..7.16.13.21.11....6..7..8.13.23.22....6..7..4.17.21.15
%e .12..2.22..4..3.21...12..9.10..2..3..4...12..9.14..2..5.21...12..2.14.11..3..9
%e .18.19..9.17.14.10...18.19.20..8.22.23...18.19.20.17.11.15...18.19.20.13.22.23
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 24 2015