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%I #4 Nov 18 2015 20:34:40
%S 0,1,1,0,2,0,1,4,4,0,1,10,4,8,1,1,16,28,6,16,0,3,56,97,104,25,32,0,1,
%T 128,333,553,505,68,64,1,3,320,1380,2232,3668,2144,112,128,0,6,784,
%U 4497,21312,30718,24370,8185,281,256,0,5,1792,16712,86812,366292,314166
%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 1,0 0,-1 1,2 or -1,1.
%C Table starts
%C .0...1....0......1........1..........1...........3...........1...........3
%C .1...2....4.....10.......16.........56.........128.........320.........784
%C .0...4....4.....28.......97........333........1380........4497.......16712
%C .0...8....6....104......553.......2232.......21312.......86812......553861
%C .1..16...25....505.....3668......30718......366292.....2509523....26091488
%C .0..32...68...2144....24370.....314166.....5469993....64600334...955403058
%C .0..64..112...8185...145761....2561017....80571013..1370091018.31774873994
%C .1.128..281..33056...905291...24729380..1220343344.31418295732
%C .0.256..856.141037..5678975..248623843.18239876421
%C .0.512.1674.570758.35331350.2294091610
%H R. H. Hardin, <a href="/A264583/b264583.txt">Table of n, a(n) for n = 1..127</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-3)
%F k=2: a(n) = 2*a(n-1)
%F k=3: [order 15]
%F k=4: a(n) = 2*a(n-1) +36*a(n-3) +9*a(n-4) -243*a(n-6) for n>7
%F k=5: [order 84]
%F k=6: [order 36] for n>40
%F Empirical for row n:
%F n=1: a(n) = a(n-3) +a(n-4) +2*a(n-5) -a(n-9) -a(n-10)
%F n=2: a(n) = 2*a(n-1) +16*a(n-5) -16*a(n-6) +32*a(n-7) -64*a(n-10)
%e Some solutions for n=4 k=4
%e ..1..2..3..7..8....1..2..3..4..8....1..2..3..7..8....1..5..3..4..8
%e ..0.10.11.12..4....0..7.11..9.13....0.10.11..9..4....6.10..0..9..2
%e ..5.15.13..6..9....5..6.16.14.18....5.15.13..6.18...11.15..7.17.18
%e .16.20.18.19.14...10.20.12.19.23...16.20.12.19.14...16.20.12.13.14
%e .21.22.23.24.17...21.22.15.24.17...21.22.23.24.17...21.22.23.24.19
%Y Column 2 is A000079(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Nov 18 2015
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