A264059 - OEIS

%I #6 Nov 10 2015 10:57:44

%S 1,2,1,4,8,1,8,64,18,1,16,216,324,45,1,32,729,2592,2025,125,1,64,3375,

%T 20736,32400,15625,320,1,128,15625,207360,518400,450000,102400,832,1,

%U 256,64000,2073600,11151360,12960000,5760000,692224,2197,1,512,262144

%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,-2.

%C Table starts

%C .1.....2.........4............8............16..............32..............64

%C .1.....8........64..........216...........729............3375...........15625

%C .1....18.......324.........2592.........20736..........207360.........2073600

%C .1....45......2025........32400........518400........11151360.......239878144

%C .1...125.....15625.......450000......12960000.......608212800.....28543426704

%C .1...320....102400......5760000.....324000000.....34260048000...3622687928896

%C .1...832....692224.....74880000....8100000000...1869178500000.431336822822500

%C .1..2197...4826809....988650000..202500000000.102920833800000

%C .1..5733..32867289..12899250000.5062500000000

%C .1.14994.224820036.168682500000

%H R. H. Hardin, <a href="/A264059/b264059.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6) +3*a(n-7) -a(n-8)

%F k=3: [order 17]

%F k=4: [order 8] for n>10

%F k=5: a(n) = 25*a(n-1) for n>3

%F Empirical for row n:

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

%F n=2: [order 12]

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

%F n=4: [order 32]

%e Some solutions for n=4 k=4

%e ..0..1..9.11..4....0..1..9.11..4....0..1.10..3..4....0..8..9..3..4

%e ..5..6..7.16..2....5..6..7..8..2....5..6.14..8..9....5.13..7..1..2

%e .17..3.19.21.14...10..3.20.13.22....2.18.12.21..7...10.11.20..6.22

%e .22..8.10.18.12...15.23.24.18.19...15.16.24.11.19...15.16.24.18.19

%e .20.13.15.23.24...12.21.14.16.17...20.13.22.23.17...12.21.14.23.17

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 02 2015