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A202197 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202197 #13 May 27 2018 08:26:19
%S A202197 450,1400,3500,7560,14700,26400,44550,71500,110110,163800,236600,
%T A202197 333200,459000,620160,823650,1077300,1389850,1771000,2231460,2783000,
%U A202197 3438500,4212000,5118750,6175260,7399350,8810200,10428400,12276000,14376560
%N A202197 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202197 Column 3 of A202202.
%H A202197 R. H. Hardin, <a href="/A202197/b202197.txt">Table of n, a(n) for n = 1..210</a>
%F A202197 Empirical: a(n) = 5*(n+5)*(n+4)*(n+3)*(n+2)^2/12.
%F A202197 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202197 G.f.: 10*x*(45 - 130*x + 185*x^2 - 144*x^3 + 59*x^4 - 10*x^5) / (1 - x)^6.
%F A202197 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A202197 (End)
%e A202197 Some solutions for n=4:
%e A202197 ..1..1..1..0..0....1..1..1..0..0....0..0..0..0..0....0..1..0..0..0
%e A202197 ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..0
%e A202197 ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..1..1..0..0
%e A202197 ..0..1..0..0..0....0..1..1..1..1....0..1..1..0..0....0..1..1..0..0
%e A202197 ..0..1..0..0..0....0..1..1..1..1....0..0..0..0..0....0..1..1..0..0
%e A202197 ..0..0..0..0..0....0..1..1..1..0....0..0..0..0..0....0..1..1..0..0
%Y A202197 Cf. A202202.
%K A202197 nonn
%O A202197 1,1
%A A202197 _R. H. Hardin_, Dec 14 2011