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A202199 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202199 #12 May 27 2018 10:31:12
%S A202199 1176,4704,14700,38808,90552,192192,378378,700700,1233232,2079168,
%T A202199 3378648,5317872,8139600,12155136,17757894,25438644,35802536,49588000,
%U A202199 67687620,91171080,121310280,159606720,207821250,268006284,342540576
%N A202199 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202199 Column 5 of A202202.
%H A202199 R. H. Hardin, <a href="/A202199/b202199.txt">Table of n, a(n) for n = 1..210</a>
%F A202199 Empirical: a(n) = 7*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/360.
%F A202199 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202199 G.f.: 14*x*(84 - 336*x + 714*x^2 - 924*x^3 + 756*x^4 - 384*x^5 + 111*x^6 - 14*x^7) / (1 - x)^8.
%F A202199 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A202199 (End)
%e A202199 Some solutions for n=2:
%e A202199 ..1..1..1..1..1..1..0....1..1..1..0..0..0..0....0..1..1..1..1..1..1
%e A202199 ..1..1..1..1..1..0..0....1..1..1..1..1..1..1....1..1..1..1..1..0..0
%e A202199 ..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..1..1..1..0..0..0
%e A202199 ..1..0..0..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0
%Y A202199 Cf. A202202.
%K A202199 nonn
%O A202199 1,1
%A A202199 _R. H. Hardin_, Dec 14 2011