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%I #6 Nov 10 2015 11:26:35
%S 2,9,4,45,40,8,144,441,169,16,512,2745,4410,714,32,1936,21025,54756,
%T 44100,3025,64,7381,167464,911754,1086300,441000,12816,128,27225,
%U 1336336,15437041,39087504,21511044,4410000,54289,256,101250,10277652,267205956
%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 0,2 or 1,1.
%C Table starts
%C ...2......9.........45..........144...........512...........1936...........7381
%C ...4.....40........441.........2745.........21025.........167464........1336336
%C ...8....169.......4410........54756........911754.......15437041......267205956
%C ..16....714......44100......1086300......39087504.....1399892079....52292712976
%C ..32...3025.....441000.....21511044....1680100825...127528266321.10275868913985
%C ..64..12816....4410000....426058380...72203451849.11613782698504
%C .128..54289...44100000...8439361956.3103083479700
%C .256.229970..441000000.167165327340
%C .512.974169.4410000000
%H R. H. Hardin, <a href="/A264110/b264110.txt">Table of n, a(n) for n = 1..71</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1) +4*a(n-3) +a(n-4)
%F k=3: a(n) = 10*a(n-1) for n>2
%F k=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4)
%F k=5: [order 14]
%F Empirical for row n:
%F n=1: [linear recurrence of order 14]
%e Some solutions for n=3 k=4
%e ..0..3..2..1..4....6..3..4..1..2....6..7..8..1..4....6..3..0..9..4
%e ..5.12..9.14..7...11..0..9.14..7....5..0..9..2..3....5..8..1..2..7
%e .10.11..6.13..8...10..5.12.13..8...16.11.10.13.14...16.13.18.11.14
%e .15.18.19.16.17...15.16.17.18.19...15.18.17.12.19...17.10.15.12.19
%Y Column 1 is A000079.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 03 2015
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