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A202200 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202200 #11 May 27 2018 11:43:19
%S A202200 1728,7680,26400,76032,192192,439296,926640,1830400,3422848,6110208,
%T A202200 10480704,17364480,27907200,43659264,66682704,99677952,146132800,
%U A202200 210496000,298378080,416782080,574367040,781747200,1051830000,1400196096
%N A202200 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202200 Column 6 of A202202.
%H A202200 R. H. Hardin, <a href="/A202200/b202200.txt">Table of n, a(n) for n = 1..210</a>
%F A202200 Empirical: a(n) = (n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/315.
%F A202200 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202200 G.f.: 16*x*(108 - 492*x + 1218*x^2 - 1890*x^3 + 1932*x^4 - 1308*x^5 + 567*x^6 - 143*x^7 + 16*x^8) / (1 - x)^9.
%F A202200 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A202200 (End)
%e A202200 Some solutions for n=2:
%e A202200 ..1..1..1..1..1..1..1..0....0..1..1..1..1..1..1..1....0..1..1..1..0..0..0..0
%e A202200 ..1..1..1..1..1..0..0..0....1..1..1..1..1..1..0..0....1..0..0..0..0..0..0..0
%e A202200 ..1..1..1..1..0..0..0..0....0..1..1..1..1..0..0..0....1..0..0..0..0..0..0..0
%e A202200 ..0..1..1..0..0..0..0..0....0..1..1..1..0..0..0..0....0..0..0..0..0..0..0..0
%Y A202200 Cf. A202202.
%K A202200 nonn
%O A202200 1,1
%A A202200 _R. H. Hardin_, Dec 14 2011