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%I #9 Jul 19 2023 10:19:28
%S 96,258,776,2201,6037,16722,46270,127161,349088,958698,2630889,
%T 7215860,19790631,54276884,148842778,408154085,1119230330,3069096344,
%U 8415836728,23077199603,63280320762,173521625446,475815066492,1304736247929
%N Number of (n+2)X3 binary arrays avoiding patterns 001 and 010 in rows, columns and nw-to-se diagonals.
%H R. H. Hardin, <a href="/A202891/b202891.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +14*a(n-3) -20*a(n-4) +9*a(n-5) -47*a(n-6) +24*a(n-7) +14*a(n-8) +62*a(n-9) +24*a(n-10) -33*a(n-11) -52*a(n-12) -43*a(n-13) +4*a(n-14) +25*a(n-15) +20*a(n-16) +5*a(n-17) -2*a(n-18) -3*a(n-19).
%e Some solutions for n=3
%e ..1..1..1....0..1..1....0..1..1....1..1..1....1..0..1....1..0..1....0..1..1
%e ..1..1..1....1..1..0....1..1..1....1..1..1....1..0..0....0..1..1....1..1..1
%e ..1..1..1....1..0..1....1..1..1....0..1..1....0..0..0....0..1..1....1..1..1
%e ..1..1..0....1..1..1....1..1..1....1..0..0....1..0..0....0..1..1....0..0..0
%e ..1..0..0....1..1..1....1..0..0....1..1..0....1..0..0....0..1..1....0..0..0
%Y Column 1 of A202898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2011