|
%I #4 Dec 03 2013 07:05:25
%S 1,2,2,5,11,5,14,74,74,14,41,515,1202,515,41,122,3602,19643,19643,
%T 3602,122,365,25211,321125,750092,321125,25211,365,1094,176474,
%U 5249894,28644884,28644884,5249894,176474,1094,3281,1235315,85827722,1093911305
%N T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 in row major order
%C Table starts
%C ....1.......2..........5............14...............41.................122
%C ....2......11.........74...........515.............3602...............25211
%C ....5......74.......1202.........19643...........321125.............5249894
%C ...14.....515......19643........750092.........28644884..........1093911305
%C ...41....3602.....321125......28644884.......2555361596........227962456547
%C ..122...25211....5249894....1093911305.....227962456547......47506658438246
%C ..365..176474...85827722...41775098873...20336458202315....9900284810558324
%C .1094.1235315.1403151863.1595338735322.1814209743962774.2063199965393914025
%H R. H. Hardin, <a href="/A233018/b233018.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F k=2: a(n) = 8*a(n-1) -7*a(n-2)
%F k=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3)
%F k=4: a(n) = 46*a(n-1) -312*a(n-2) +530*a(n-3) -263*a(n-4)
%F k=5: [order 8]
%F k=6: [order 14]
%F k=7: [order 33]
%e Some solutions for n=3 k=4
%e ..0..1..1..1....0..0..1..3....0..1..1..1....0..1..3..1....0..0..0..1
%e ..1..1..1..1....0..1..3..1....1..1..3..1....1..3..2..0....2..0..2..0
%e ..0..1..1..0....0..1..3..3....1..1..3..3....1..1..3..1....0..0..2..2
%Y Column 1 is A007051(n-1)
%Y Column 2 is A199417(n-1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 03 2013
| 