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A264244
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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.
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13
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2, 8, 3, 21, 21, 5, 57, 95, 89, 8, 164, 557, 804, 296, 13, 460, 3303, 9005, 5055, 1105, 21, 1289, 18725, 108020, 119737, 36193, 3897, 34, 3629, 105839, 1249237, 2982248, 1696877, 243881, 14128, 55, 10202, 602365, 14586353, 70618408, 86191713
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OFFSET
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1,1
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COMMENTS
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Table starts
..2......8.......21..........57............164.............460.............1289
..3.....21.......95.........557...........3303...........18725...........105839
..5.....89......804........9005.........108020.........1249237.........14586353
..8....296.....5055......119737........2982248........70618408.......1687935233
.13...1105....36193.....1696877.......86191713......4157973485.....203949869341
.21...3897...243881....23471441.....2448948509....240749059561...24147725322385
.34..14128..1688581...327315125....69880683436..13986284450284.2870671705359089
.55..50533.11546272..4550623993..1990480615856.810930428170425
.89.181937.79399773.63332634829.56719203638885
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) +6*a(n-2) -a(n-3)
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)
k=4: [order 18]
k=5: [order 48]
Empirical for row n:
n=1: a(n)=2*a(n-1)+a(n-2)+4*a(n-3)-a(n-4)-a(n-6)
n=2: [order 9] for n>10
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EXAMPLE
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Some solutions for n=4 k=4
..1..5..2..3..4....1..5..2..7..4....1..2..6..3..4....0..1..4..3..8
..6..0..7..8..9....6..0..9..8..3....7..0.11..9.13....5..6..9..2.13
.10.12.16.17.14...10.13.12.14.18...10..5.12.14..8...10.11.12..7.14
.15.20.11.19.13...16.20.11.19.23...15.17.21.19.23...17.16.21.18.19
.21.23.22.24.18...21.15.22.17.24...20.22.16.24.18...20.15.22.23.24
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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