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%I #4 Nov 11 2015 13:18:28
%S 0,1,1,1,2,1,1,4,4,1,2,8,11,8,2,3,16,40,40,16,3,4,32,133,240,133,32,4,
%T 6,64,464,1528,1528,464,64,6,9,128,1573,8976,15040,8976,1573,128,9,13,
%U 256,5373,51904,144289,144289,51904,5373,256,13,19,512,18376,302328,1371555
%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,1 1,0 1,-1 or 0,-1.
%C Table starts
%C ..0...1.....1........1..........2............3..............4................6
%C ..1...2.....4........8.........16...........32.............64..............128
%C ..1...4....11.......40........133..........464...........1573.............5373
%C ..1...8....40......240.......1528.........8976..........51904...........302328
%C ..2..16...133.....1528......15040.......144289........1371555.........13030122
%C ..3..32...464.....8976.....144289......2464988.......40119900........640302232
%C ..4..64..1573....51904....1371555.....40119900.....1082465413......28865247648
%C ..6.128..5373...302328...13030122....640302232....28865247648....1305850666324
%C ..9.256.18376..1757848..123154946..10206221300...765329377660...57981524413360
%C .13.512.62754.10199400.1162675576.162325629616.20139599598080.2544934124095448
%H R. H. Hardin, <a href="/A264336/b264336.txt">Table of n, a(n) for n = 1..264</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-3)
%F k=2: a(n) = 2*a(n-1)
%F k=3: [order 14]
%F k=4: a(n) = 6*a(n-1) -5*a(n-2) +36*a(n-3) -72*a(n-4) -243*a(n-6) for n>7
%F k=5: [order 84]
%F k=6: [order 36] for n>38
%e Some solutions for n=4 k=4
%e ..1..5..3..4..8....1..2..6..7..8....1..2..6..7..8....1..2..6..4..8
%e ..0..7..2.12.13....0.10..3.12..4....0.10.11..3..4....0.10..3.12.13
%e .11..6.16..9.18....5.15.16.14..9....5.12.13.14..9....5.15..7.17..9
%e .10.20.21.14.23...11.20.13.22.23...16.20.21.22.23...11.20.18.22.14
%e .15.22.17.24.19...21.17.18.24.19...15.17.18.24.19...21.16.23.24.19
%Y Column 1 is A000930(n-2).
%Y Column 2 is A000079(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Nov 11 2015
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