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A202198 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202198 #14 May 27 2018 08:26:51
%S A202198 756,2688,7560,18144,38808,76032,138996,240240,396396,628992,965328,
%T A202198 1439424,2093040,2976768,4151196,5688144,7671972,10200960,13388760,
%U A202198 17365920,22281480,28304640,35626500,44461872,55051164,67662336,82592928
%N A202198 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202198 Column 4 of A202202.
%H A202198 R. H. Hardin, <a href="/A202198/b202198.txt">Table of n, a(n) for n = 1..210</a>
%F A202198 Empirical: a(n) = (n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/10.
%F A202198 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202198 G.f.: 12*x*(63 - 217*x + 385*x^2 - 399*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.
%F A202198 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A202198 (End)
%e A202198 Some solutions for n=3:
%e A202198 ..0..1..1..1..1..1....1..1..1..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
%e A202198 ..1..1..1..1..1..1....1..1..1..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
%e A202198 ..0..1..1..1..0..0....1..1..0..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
%e A202198 ..0..1..1..0..0..0....1..1..0..0..0..0....0..1..1..0..0..0....1..1..1..0..0..0
%e A202198 ..0..1..1..0..0..0....1..1..0..0..0..0....0..1..1..0..0..0....0..1..1..0..0..0
%Y A202198 Cf. A202202.
%K A202198 nonn
%O A202198 1,1
%A A202198 _R. H. Hardin_, Dec 14 2011