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A203084 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 101 in rows and columns.

%I A203084 #11 Mar 03 2018 05:35:26
%S A203084 98,253,621,1575,4000,10057,25384,64140,161819,408415,1031041,2602296,
%T A203084 6568305,16579362,41847510,105626421,266611217,672949667,1698582936,
%U A203084 4287374163,10821707646,27314936026,68945297129,174023973205
%N A203084 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 101 in rows and columns.
%C A203084 Column 1 of A203091.
%H A203084 R. H. Hardin, <a href="/A203084/b203084.txt">Table of n, a(n) for n = 1..210</a>
%F A203084 Empirical: a(n) = a(n-1) + a(n-2) + 6*a(n-3) + 2*a(n-4) + 3*a(n-5) - a(n-6) - a(n-8) - a(n-9) - a(n-10).
%F A203084 Empirical g.f.: x*(98 + 155*x + 270*x^2 + 113*x^3 + 90*x^4 - 44*x^5 - 26*x^6 - 61*x^7 - 53*x^8 - 36*x^9) / (1 - x - x^2 - 6*x^3 - 2*x^4 - 3*x^5 + x^6 + x^8 + x^9 + x^10). - _Colin Barker_, Mar 03 2018
%e A203084 Some solutions for n=3:
%e A203084   1 0 0    1 1 0    1 1 0    0 1 0    0 0 1    1 1 1    1 0 0
%e A203084   1 1 0    1 1 0    1 1 1    1 0 0    1 1 1    1 1 0    1 1 0
%e A203084   1 1 1    1 1 1    1 1 1    0 0 1    1 0 0    1 1 0    0 1 1
%e A203084   1 1 1    0 1 1    1 1 1    0 1 1    1 0 0    0 1 1    0 1 1
%e A203084   0 1 0    0 0 1    0 1 0    1 1 0    0 1 1    0 0 1    1 0 0
%Y A203084 Cf. A203091.
%K A203084 nonn
%O A203084 1,1
%A A203084 _R. H. Hardin_, Dec 29 2011