%I #6 Nov 10 2015 12:27:18
%S 1,6,4,12,134,18,31,1992,3035,70,89,27650,145151,69084,292,230,343431,
%T 8296414,14088801,1643235,1212,536,3777963,479355276,3822509358,
%U 1544467524,38562523,5028,1171,38762619,24453863816,1035523589834
%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 filled by rows with each element moved a city block distance of 1 or 2, and rows and columns in increasing lexicographic order.
%C Table starts
%C .....1.........6...........12............31............89.............230
%C .....4.......134.........1992.........27650........343431.........3777963
%C ....18......3035.......145151.......8296414.....479355276.....24453863816
%C ....70.....69084.....14088801....3822509358.1035523589834.244734723702847
%C ...292...1643235...1544467524.1954083613268
%C ..1212..38562523.162168224979
%C ..5028.903637375
%C .20832
%H R. H. Hardin, <a href="/A263586/b263586.txt">Table of n, a(n) for n = 1..40</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) +2*a(n-3) +4*a(n-4) -8*a(n-5)
%F k=2: [order 84]
%F Empirical for row n:
%F n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -2*a(n-5) +3*a(n-6) -a(n-8) for n>9
%e Some solutions for n=3 k=4
%e ..1..3..4..7..9....1..5..7..9.14....1..3..4..7..9....1..5..7..8..9
%e ..6..0..5..2..8....6..0..2.12..4....6..0..5..2..8....6..0.12.13..3
%e .11.15.10.19.12...11.15..8..3.13...11.15.10.19.18...11.15..2.14..4
%e .16.17.18.13.14...17.10.16.19.18...17.12.16.13.14...17.10.19.16.18
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Oct 22 2015