|
%I #4 Dec 05 2013 06:27:18
%S 1,1,1,3,1,3,11,8,8,11,48,64,96,64,48,236,512,1280,1280,512,236,1248,
%T 4096,18432,28672,18432,4096,1248,6896,32768,278528,720896,720896,
%U 278528,32768,6896,39168,262144,4325376,19922944,31457280,19922944,4325376
%N T(n,k)=Number of nXk 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs)
%C Table starts
%C ......1........1...........3.............11................48
%C ......1........1...........8.............64...............512
%C ......3........8..........96...........1280.............18432
%C .....11.......64........1280..........28672............720896
%C .....48......512.......18432.........720896..........31457280
%C ....236.....4096......278528.......19922944........1543503872
%C ...1248....32768.....4325376......587202560.......83751862272
%C ...6896...262144....68157440....17985175552.....4879082848256
%C ..39168..2097152..1082130432...562640715776...296868139499520
%C .226496.16777216.17246978048.17798344474624.18506979718725632
%H R. H. Hardin, <a href="/A233168/b233168.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical for column k:
%F k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4
%F k=2: a(n) = 8*a(n-1) for n>2
%F k=3: a(n) = 24*a(n-1) -128*a(n-2) for n>3
%F k=4: a(n) = 48*a(n-1) -512*a(n-2) for n>3
%F k=5: a(n) = 96*a(n-1) -2048*a(n-2) for n>3
%F k=6: a(n) = 192*a(n-1) -8192*a(n-2) for n>3
%F k=7: a(n) = 384*a(n-1) -32768*a(n-2) for n>3
%e Some solutions for n=4 k=4
%e ..0..1..2..3....0..1..7..1....0..1..7..6....0..1..7..2....0..1..0..6
%e ..2..4..0..1....2..3..5..3....2..3..5..4....3..2..3..1....2..3..2..4
%e ..7..6..5..3....7..6..0..6....6..0..1..0....7..1..7..5....0..1..0..6
%e ..2..4..0..6....3..2..3..5....4..2..3..5....4..5..4..6....3..5..3..2
%Y Column 2 is A001018(n-2)
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 05 2013
| 