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A264128
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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 index change +-(.,.) 0,0 1,-2 or 2,-1.
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8
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1, 2, 2, 4, 9, 4, 8, 45, 45, 8, 16, 200, 576, 200, 16, 32, 845, 5733, 5733, 845, 32, 64, 3549, 53361, 108045, 53361, 3549, 64, 128, 14994, 533610, 1995525, 1995525, 533610, 14994, 128, 256, 63525, 5336100, 39592980, 79655625, 39592980, 5336100, 63525
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.......2..........4.............8................16...................32
...2.......9.........45...........200...............845.................3549
...4......45........576..........5733.............53361...............533610
...8.....200.......5733........108045...........1995525.............39592980
..16.....845......53361.......1995525..........79655625...........3436012800
..32....3549.....533610......39592980........3436012800.........317072810421
..64...14994....5336100.....791859600......149787576576.......29534515247673
.128...63525...53361000...15730470000.....6432597984690.....2680755598121436
.256..269225..533610000..311564912400...275389278850449...242847274755986037
.512.1140624.5336100000.6168985265520.11834412715370304.22110137158388985792
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) +16*a(n-4) +4*a(n-5) +a(n-6) -4*a(n-7) -a(n-8)
k=3: a(n) = 10*a(n-1) for n>5
k=4: [order 8] for n>11
k=5: [order 32] for n>34
k=6: [order 95] for n>99
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..5..3.13....0..1..2..3.13....0..1..2..3..4....0..1..2..3..7
..2..6.16.11.18....5.15.16..8.18....5..6..7.11..9....5.15.16..8.18
.10.20.15..4.23...10.11..9..4.23...10..8.21.13.14...10.11.21..4.23
.12..7..8..9.19....6..7.17.21.22...15.16.17.18.22....6.13.17..9.22
.17.21.22.14.24...20.12.19.14.24...20.12.19.23.24...20.12.19.14.24
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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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