A208103 - OEIS

%I #8 Mar 06 2018 14:59:20

%S 6,36,78,171,406,990,2485,6328,16290,42195,109746,286146,747253,

%T 1953276,5108806,13367035,34982430,91564278,239684565,627447600,

%U 1642590586,4300214691,11257876378,29473127866,77161043541,202009252500

%N Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.

%C Column 3 of A208108.

%H R. H. Hardin, <a href="/A208103/b208103.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 6*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) for n>7.

%F Empirical g.f.: x*(6 + 12*x - 54*x^2 - 33*x^3 + 70*x^4 + 20*x^5 - 15*x^6) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - _Colin Barker_, Mar 06 2018

%e Some solutions for n=10:

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

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

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

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

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

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

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

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

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

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

%Y Cf. A208108.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012