|
%I #4 Dec 06 2013 16:27:28
%S 1,1,3,3,10,11,10,104,136,48,36,1184,4672,2080,236,136,13952,166400,
%T 221696,32896,1248,528,166400,6049792,23896064,10620928,524800,6896,
%U 2080,1992704,220626944,2647261184,3439984640,509640704,8390656,39168,8256
%N T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs)
%C Table starts
%C .......1...........1................3....................10
%C .......3..........10..............104..................1184
%C ......11.........136.............4672................166400
%C ......48........2080...........221696..............23896064
%C .....236.......32896.........10620928............3439984640
%C ....1248......524800........509640704..........495341010944
%C ....6896.....8390656......24461443072........71328837140480
%C ...39168...134225920....1174138781696.....10271348253261824
%C ..226496..2147516416...56358577635328...1479074079750225920
%C .1325568.34359869440.2705211055407104.212986666384520904704
%H R. H. Hardin, <a href="/A233256/b233256.txt">Table of n, a(n) for n = 1..240</a>
%F Empirical for column k:
%F k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
%F k=2: a(n) = 20*a(n-1) -64*a(n-2)
%F k=3: a(n) = 56*a(n-1) -384*a(n-2)
%F k=4: a(n) = 160*a(n-1) -2304*a(n-2)
%F k=5: a(n) = 512*a(n-1) -33792*a(n-2) +589824*a(n-3)
%F k=6: a(n) = 1664*a(n-1) -471040*a(n-2) +44826624*a(n-3) -1358954496*a(n-4)
%F k=7: [order 5]
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
%F n=2: a(n) = 16*a(n-1) -48*a(n-2) for n>3
%F n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3) for n>5
%F n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4) for n>8
%F n=5: [order 7] for n>11
%F n=6: [order 10] for n>16
%F n=7: [order 28] for n>34
%e Some solutions for n=3 k=4
%e ..0..1..0..2....0..1..0..2....0..1..2..4....0..1..0..2....0..1..2..4
%e ..5..3..5..2....2..1..0..4....3..4..2..4....3..4..0..4....2..0..3..1
%e ..4..3..1..5....5..2..0..3....3..1..5..4....3..1..5..1....4..0..2..0
%Y Column 1 is A233162(n+1)
%Y Column 2 is A026244(n-1)
%Y Row 1 is A007582(n-2)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Dec 06 2013
| 