A207559 - OEIS

%I #8 Mar 05 2018 09:27:53

%S 6,36,92,221,618,1690,4861,13900,40452,117717,345002,1012682,2983173,

%T 8803252,26036140,77123437,228815946,679742490,2021736365,6019369820,

%U 17938267476,53500929061,159681492682,476893979146,1425053001333

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

%C Column 3 of A207564.

%H R. H. Hardin, <a href="/A207559/b207559.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 21*a(n-3) + 36*a(n-4) + 12*a(n-5) - 39*a(n-6) + 6*a(n-7) + 10*a(n-8) - 3*a(n-9) for n>10.

%F Empirical g.f.: x*(6 - 88*x^2 + 11*x^3 + 384*x^4 - 128*x^5 - 440*x^6 + 160*x^7 + 120*x^8 - 45*x^9) / ((1 - x)*(1 + x)*(1 - 3*x)*(1 - 3*x + x^2)*(1 + x - x^2)*(1 - x - x^2)). - _Colin Barker_, Mar 05 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207564.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 18 2012