|
%I #6 Nov 27 2015 05:26:21
%S 1,3,3,9,17,9,27,99,99,27,81,577,1163,577,81,243,3363,13707,13707,
%T 3363,243,729,19601,161621,328989,161621,19601,729,2187,114243,
%U 1905737,7915555,7915555,1905737,114243,2187,6561,665857,22471303,190528543
%N T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically or antidiagonally, and top left element zero
%C Table starts
%C .....1........3...........9.............27.................81
%C .....3.......17..........99............577...............3363
%C .....9.......99........1163..........13707.............161621
%C ....27......577.......13707.........328989............7915555
%C ....81.....3363......161621........7915555..........389997789
%C ...243....19601.....1905737......190528543........19245039957
%C ...729...114243....22471303.....4586348177.......950054488141
%C ..2187...665857...264968059...110402289283.....46905123394619
%C ..6561..3880899..3124343613..2657600587981...2315805078150557
%C .19683.22619537.36840376337.63973693477099.114336803085406731
%H R. H. Hardin, <a href="/A232948/b232948.txt">Table of n, a(n) for n = 1..264</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1)
%F k=2: a(n) = 6*a(n-1) -a(n-2)
%F k=3: a(n) = 13*a(n-1) -15*a(n-2) +9*a(n-3) -2*a(n-4) for n>5, A232943.
%F k=4: [order 10] for n>11, A232944.
%F k=5: [order 21] for n>23, A232945.
%F k=6: [order 57] for n>59
%e Some solutions for n=3 k=4
%e ..0..2..3..2....0..2..3..2....0..2..3..3....0..1..1..0....0..2..3..3
%e ..2..3..3..3....0..2..2..0....2..3..3..1....1..1..1..1....0..2..2..2
%e ..2..2..3..2....2..0..2..2....2..2..3..1....3..3..1..0....0..2..0..2
%Y Column 1 is A000244(n-1)
%Y Column 2 is A001541
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 02 2013
| 