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%I #8 Nov 10 2015 11:50:01
%S 2,8,3,21,21,5,57,95,89,8,164,557,804,296,13,460,3303,9005,5055,1105,
%T 21,1289,18725,108020,119737,36193,3897,34,3629,105839,1249237,
%U 2982248,1696877,243881,14128,55,10202,602365,14586353,70618408,86191713
%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 0,0 1,1 0,-1 -1,1 or 0,-2.
%C Table starts
%C ..2......8.......21..........57............164.............460.............1289
%C ..3.....21.......95.........557...........3303...........18725...........105839
%C ..5.....89......804........9005.........108020.........1249237.........14586353
%C ..8....296.....5055......119737........2982248........70618408.......1687935233
%C .13...1105....36193.....1696877.......86191713......4157973485.....203949869341
%C .21...3897...243881....23471441.....2448948509....240749059561...24147725322385
%C .34..14128..1688581...327315125....69880683436..13986284450284.2870671705359089
%C .55..50533.11546272..4550623993..1990480615856.810930428170425
%C .89.181937.79399773.63332634829.56719203638885
%H R. H. Hardin, <a href="/A264244/b264244.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) +6*a(n-2) -a(n-3)
%F k=3: a(n) = 7*a(n-1) +7*a(n-2) -65*a(n-3) +65*a(n-4) +62*a(n-5) -72*a(n-6)
%F k=4: [order 18]
%F k=5: [order 48]
%F Empirical for row n:
%F n=1: a(n)=2*a(n-1)+a(n-2)+4*a(n-3)-a(n-4)-a(n-6)
%F n=2: [order 9] for n>10
%e Some solutions for n=4 k=4
%e ..1..5..2..3..4....1..5..2..7..4....1..2..6..3..4....0..1..4..3..8
%e ..6..0..7..8..9....6..0..9..8..3....7..0.11..9.13....5..6..9..2.13
%e .10.12.16.17.14...10.13.12.14.18...10..5.12.14..8...10.11.12..7.14
%e .15.20.11.19.13...16.20.11.19.23...15.17.21.19.23...17.16.21.18.19
%e .21.23.22.24.18...21.15.22.17.24...20.22.16.24.18...20.15.22.23.24
%Y Column 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 09 2015
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