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%I #6 Nov 10 2015 10:47:07
%S 2,5,4,13,21,8,34,121,89,16,89,605,1210,377,32,233,3025,12100,12100,
%T 1597,64,610,15125,131890,239580,121000,6765,128,1597,75625,1445345,
%U 5645376,4745620,1210000,28657,256,4181,378125,15892745,130697424,242621698
%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 index change +-(.,.) 0,0 0,1 or 1,2.
%C Table starts
%C ....2.......5..........13.............34................89..................233
%C ....4......21.........121............605..............3025................15125
%C ....8......89........1210..........12100............131890..............1445345
%C ...16.....377.......12100.........239580...........5645376............130697424
%C ...32....1597......121000........4745620.........242621698..........11909009849
%C ...64....6765.....1210000.......94000060.......10427064769........1084282319384
%C ..128...28657....12100000.....1861931060......448121165789.......98725402363225
%C ..256..121393...121000000....36880691100....19258783041289.....8989061417123964
%C ..512..514229..1210000000...730524027860...827679549612058...818464496640651553
%C .1024.2178309.12100000000.14470047586940.35570961850254336.74522143720797473932
%H R. H. Hardin, <a href="/A264071/b264071.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1) +a(n-2)
%F k=3: a(n) = 10*a(n-1) for n>2
%F k=4: a(n) = 19*a(n-1) +16*a(n-2) for n>3
%F k=5: a(n) = 43*a(n-1) -43*a(n-3) +a(n-4) for n>5
%F k=6: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5) for n>7
%F k=7: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5) for n>8
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) -a(n-2)
%F n=2: a(n) = 5*a(n-1) for n>3
%F n=3: a(n) = 12*a(n-1) -12*a(n-2) +12*a(n-3) -12*a(n-4) +a(n-5) for n>7
%F n=4: a(n) = 24*a(n-1) -19*a(n-2) -11*a(n-3) +36*a(n-4) +3*a(n-5) for n>9
%F n=5: [order 14] for n>19
%F n=6: [order 10] for n>19
%e Some solutions for n=3 k=4
%e ..0..8..9..3..4....6..1..2..3..4....7..8..2..3..4....0..8..2..3..4
%e ..5.13..7..1..2...11.13..0..8..9...12..6..0..1..9....5..6..7..1..9
%e .16.11.18..6.14...10..5.19..7.14...17..5.18.13.14...17.18.12.13.14
%e .15.10.17.12.19...15.16.17.18.12...15.16.10.11.19...15.16.10.11.19
%Y Column 1 is A000079.
%Y Column 2 is A015448(n+1).
%Y Row 1 is A001519(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 02 2015
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