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A264676
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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 -1,-1 1,0 -1,-2 -2,-2 or 0,1.
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14
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0, 1, 1, 1, 2, 0, 1, 10, 9, 0, 1, 29, 34, 19, 1, 3, 75, 123, 145, 44, 0, 3, 201, 748, 890, 603, 108, 0, 4, 588, 3698, 9205, 6851, 2417, 264, 1, 6, 1700, 17443, 88687, 123222, 43131, 9976, 649, 0, 9, 4785, 84737, 714235, 2025372, 1449467, 291315, 40825, 1573, 0, 12
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OFFSET
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1,5
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COMMENTS
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Table starts
.0....1......1........1...........1.............3..............3
.1....2.....10.......29..........75...........201............588
.0....9.....34......123.........748..........3698..........17443
.0...19....145......890........9205.........88687.........714235
.1...44....603.....6851......123222.......2025372.......29875350
.0..108...2417....43131.....1449467......43095017.....1095840260
.0..264...9976...291315....17406354.....918298857....40765995197
.1..649..40825..1980287...209749118...19297801298..1494347569074
.0.1573.166985.13199209..2503676777..404856272120.54204721906375
.0.3837.684253.88670692.29934965340.8489260394876
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-3)
k=2: a(n) = 2*a(n-1) +a(n-3) +3*a(n-4) +2*a(n-5) -a(n-6) +4*a(n-7) -a(n-8) -a(n-10)
k=3: [order 15]
k=4: [order 26] for n>27
Empirical for row n:
n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)
n=2: [order 9]
n=3: [order 70]
n=4: [order 81] for n>86
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EXAMPLE
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Some solutions for n=4 k=4
..6..8..1..2..3....7..8..1..2..3...12..8..1..2..3...12.13..1..2..3
..0..5.14..7..4....0.13..6.14..4....0..5..6..7..4....0.18.19..7..4
.16.10.24.19..9....5.23.24.12..9...17.18.24.19..9....5..6.24..8..9
.21.11.12.13.18...10.11.16.17.18...10.11.16.13.14...10.11.16.17.14
.15.20.17.22.23...15.20.21.22.19...15.20.21.22.23...15.20.21.22.23
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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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