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A202048 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.

%I A202048 #10 May 25 2018 12:21:27
%S A202048 636,1968,4980,11016,22092,41088,71964,120000,192060,296880,445380,
%T A202048 651000,930060,1302144,1790508,2422512,3230076,4250160,5525268,
%U A202048 7103976,9041484,11400192,14250300,17670432,21748284,26581296,32277348,38955480
%N A202048 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.
%C A202048 Column 4 of A202052.
%H A202048 R. H. Hardin, <a href="/A202048/b202048.txt">Table of n, a(n) for n = 1..210</a>
%F A202048 Empirical: a(n) = (1/30)*n^6 + (9/10)*n^5 + (59/6)*n^4 + (111/2)*n^3 + (2552/15)*n^2 + (1278/5)*n + 144.
%F A202048 Conjectures from _Colin Barker_, May 25 2018: (Start)
%F A202048 G.f.: 12*x*(53 - 207*x + 380*x^2 - 398*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.
%F A202048 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 A202048 (End)
%e A202048 Some solutions for n=3:
%e A202048 ..0..1..0..0..0..0....0..0..0..0..0..0....1..0..1..0..1..0....1..0..0..0..0..0
%e A202048 ..1..0..0..0..0..0....1..0..1..0..1..1....0..1..0..1..0..0....1..0..1..1..1..1
%e A202048 ..0..1..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0
%e A202048 ..1..0..0..0..0..0....1..0..1..0..1..1....0..0..0..0..0..0....1..0..1..1..1..1
%e A202048 ..0..0..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0....1..0..1..1..1..1
%Y A202048 Cf. A202052.
%K A202048 nonn
%O A202048 1,1
%A A202048 _R. H. Hardin_, Dec 10 2011