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A264017
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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 2,2.
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10
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1, 2, 1, 4, 5, 1, 8, 25, 13, 1, 16, 105, 169, 34, 1, 32, 441, 1573, 1156, 89, 1, 64, 1869, 14641, 20570, 7921, 233, 1, 128, 7921, 146410, 366025, 269225, 54289, 610, 1, 256, 33553, 1464100, 7320500, 9150625, 3524125, 372100, 1597, 1, 512, 142129, 14641000
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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..................64
.1....5.......25........105...........441.............1869................7921
.1...13......169.......1573.........14641...........146410.............1464100
.1...34.....1156......20570........366025..........7320500...........146410000
.1...89.....7921.....269225.......9150625........398967250.........17394972100
.1..233....54289....3524125.....228765625......21860843125.......2089022169025
.1..610...372100...46131250....5719140625....1201888840625.....252579343635025
.1.1597..2550409..603865625..142978515625...66099082156250...30557658560100100
.1.4181.17480761.7904703125.3574462890625.3635200164062500.3696969485250250000
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..143
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 8*a(n-1) -8*a(n-2) +a(n-3)
k=4: a(n) = 15*a(n-1) -25*a(n-2) for n>4
k=5: a(n) = 25*a(n-1) for n>3
k=6: a(n) = 60*a(n-1) -300*a(n-2) +1500*a(n-3) -7500*a(n-4) +3125*a(n-5) for n>7
k=7: [order 13] for n>15
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1) +4*a(n-3) +a(n-4)
n=3: a(n) = 10*a(n-1) for n>5
n=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4) for n>8
n=5: [order 14] for n>18
n=6: [order 25] for n>31
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EXAMPLE
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Some solutions for n=4 k=4
..0..8..9..3..4....0.13..2..3..4....7..1.14..3..4....7..1.14..3..4
..5.13.14..1..2...12..6..7..8..9...17..6..0..8..9...12.13..0..8..9
.17.18.12..6..7...22.23.24..1.14...10.11..5.13..2...17.18..5..6..2
.15.16.10.11.19...15.16..5.18.19...15.23.24.18.19...15.16.10.11.19
.20.21.22.23.24...20.21.10.11.17...20.21.22.16.12...20.21.22.23.24
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CROSSREFS
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Column 2 is A001519(n+1).
Column 3 is A081068.
Row 1 is A000079(n-1).
Sequence in context: A143494 A124960 A137346 * A159971 A114158 A248666
Adjacent sequences: A264014 A264015 A264016 * A264018 A264019 A264020
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Nov 01 2015
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STATUS
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approved
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