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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

%I #6 Nov 10 2015 11:03:29

%S 1,2,2,4,9,4,8,45,45,8,16,200,576,200,16,32,845,5733,5733,845,32,64,

%T 3549,53361,108045,53361,3549,64,128,14994,533610,1995525,1995525,

%U 533610,14994,128,256,63525,5336100,39592980,79655625,39592980,5336100,63525

%N 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.

%C Table starts

%C ...1.......2..........4.............8................16...................32

%C ...2.......9.........45...........200...............845.................3549

%C ...4......45........576..........5733.............53361...............533610

%C ...8.....200.......5733........108045...........1995525.............39592980

%C ..16.....845......53361.......1995525..........79655625...........3436012800

%C ..32....3549.....533610......39592980........3436012800.........317072810421

%C ..64...14994....5336100.....791859600......149787576576.......29534515247673

%C .128...63525...53361000...15730470000.....6432597984690.....2680755598121436

%C .256..269225..533610000..311564912400...275389278850449...242847274755986037

%C .512.1140624.5336100000.6168985265520.11834412715370304.22110137158388985792

%H R. H. Hardin, <a href="/A264128/b264128.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F 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)

%F k=3: a(n) = 10*a(n-1) for n>5

%F k=4: [order 8] for n>11

%F k=5: [order 32] for n>34

%F k=6: [order 95] for n>99

%e Some solutions for n=4 k=4

%e ..0..1..5..3.13....0..1..2..3.13....0..1..2..3..4....0..1..2..3..7

%e ..2..6.16.11.18....5.15.16..8.18....5..6..7.11..9....5.15.16..8.18

%e .10.20.15..4.23...10.11..9..4.23...10..8.21.13.14...10.11.21..4.23

%e .12..7..8..9.19....6..7.17.21.22...15.16.17.18.22....6.13.17..9.22

%e .17.21.22.14.24...20.12.19.14.24...20.12.19.23.24...20.12.19.14.24

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 03 2015

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Last modified April 15 11:27 EDT 2024. Contains 371681 sequences. (Running on oeis4.)