%I #8 Jun 01 2018 06:02:13

%S 198,518,1084,2232,4901,10584,22525,48429,104282,223728,480328,

%T 1032213,2217044,4761249,10227241,21967770,47183252,101344728,

%U 217680229,467553984,1004256629,2157044997,4633115818,9951459720,21374732936

%N Number of (n+2) X 4 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

%C Column 2 of A202532.

%H R. H. Hardin, <a href="/A202526/b202526.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>9.

%F Empirical g.f.: x*(198 + 122*x + 48*x^2 - 332*x^3 - 203*x^4 + 46*x^5 + 97*x^6 + 11*x^7 + 4*x^8) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A202532.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2011