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%I #4 Nov 12 2015 07:01:27
%S 1,3,1,9,6,1,18,36,13,1,36,120,169,28,1,78,400,936,784,60,1,169,1440,
%T 5184,7168,3600,129,1,364,5184,33408,65536,54720,16641,277,1,784,
%U 18432,215296,730368,831744,418992,76729,595,1,1680,65536,1323792,8139609
%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 0,2 1,0 or -1,-2.
%C Table starts
%C .1....3.......9.........18...........36.............78.............169
%C .1....6......36........120..........400...........1440............5184
%C .1...13.....169........936.........5184..........33408..........215296
%C .1...28.....784.......7168........65536.........730368.........8139609
%C .1...60....3600......54720.......831744.......16066704.......310358689
%C .1..129...16641.....418992.....10549504......353333680.....11834176225
%C .1..277...76729....3204336....133818624.....7767356736....450847788304
%C .1..595..354025...24514000...1697440000...170773835200..17180991840016
%C .1.1278.1633284..187528608..21531453696..3754476071280.654674355426025
%C .1.2745.7535025.1434558960.273119121664.82543032602992
%H R. H. Hardin, <a href="/A264364/b264364.txt">Table of n, a(n) for n = 1..127</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F k=3: a(n) = 3*a(n-1) +7*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -a(n-6)
%F k=4: a(n) = 3*a(n-1) +28*a(n-2) +57*a(n-3) +10*a(n-4) -24*a(n-5) +8*a(n-6)
%F k=5: a(n) = 11*a(n-1) +22*a(n-2) -8*a(n-3)
%F k=6: [order 30]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9)
%F n=2: a(n) = 3*a(n-1) +6*a(n-3) +4*a(n-4)
%e Some solutions for n=4 k=4
%e ..0..1..2..3..4....7..8..0..3..2....0..8..2..1..4....0..1..2..3..4
%e .12..6..7..8..9...12..1..5..6..4...12.13.14..3..7...12..6.14..8..7
%e ..5.18.19.11.14...17.18.10.13..9....5..6.19.11..9....5.11.10.13..9
%e .10.16.24.13.17...22.11.24.16.14...10.16.24.18.17...15.23.24.16.19
%e .15.21.20.23.22...15.21.20.23.19...15.21.20.23.22...20.21.17.18.22
%Y Column 2 is A002478(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 12 2015
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