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A264128 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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..127

FORMULA

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

EXAMPLE

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

CROSSREFS

Column 1 is A000079(n-1).

Sequence in context: A220313 A021982 A165251 * A176159 A280859 A280961

Adjacent sequences:  A264125 A264126 A264127 * A264129 A264130 A264131

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 03 2015

STATUS

approved

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Last modified December 3 08:07 EST 2021. Contains 349445 sequences. (Running on oeis4.)