A189337 - OEIS

%I #5 Mar 31 2012 12:36:15

%S 8,64,512,3375,21952,140608,912673,5929741,38614472,251239591,

%T 1634691752,10633486599,69173457625,449983383247,2927275422625,

%U 19042718961664,123878371625000,805862864751112,5242361459792813,34103003909455872

%N Number of nX3 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally

%C Column 3 of A189343

%H R. H. Hardin, <a href="/A189337/b189337.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 7*a(n-1) -41*a(n-3) +130*a(n-4) +81*a(n-6) -369*a(n-7) -73*a(n-8) -173*a(n-9) +243*a(n-10) +211*a(n-11) -77*a(n-12) +117*a(n-13) +81*a(n-14) +20*a(n-16) +13*a(n-17) +a(n-19) +a(n-20)

%e Some solutions for 4X3

%e ..0..1..0....0..0..0....0..0..1....0..0..0....1..1..1....1..0..1....1..1..0

%e ..0..1..1....1..1..1....1..1..0....0..0..0....1..0..1....0..1..1....1..1..1

%e ..0..1..1....0..0..1....0..1..0....0..0..0....1..1..0....1..0..1....0..1..1

%e ..1..1..1....0..0..0....1..0..0....0..1..0....0..1..1....0..0..1....1..1..1

%Y A049864(n+2) cubed

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 20 2011