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A202201 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202201 #12 May 27 2018 11:44:13
%S A202201 2430,11880,44550,138996,378378,926640,2084940,4375800,8664084,
%T A202201 16325712,29476980,51279480,86337900,141210432,225054126,350430300,
%U A202201 534298050,799227000,1174863690,1699689420,2423110950,3407929200,4733235000
%N A202201 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202201 Column 7 of A202202.
%H A202201 R. H. Hardin, <a href="/A202201/b202201.txt">Table of n, a(n) for n = 1..210</a>
%F A202201 Empirical: a(n) = (n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/2240.
%F A202201 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202201 G.f.: 18*x*(135 - 690*x + 1950*x^2 - 3528*x^3 + 4326*x^4 - 3660*x^5 + 2115*x^6 - 800*x^7 + 179*x^8 - 18*x^9) / (1 - x)^10.
%F A202201 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F A202201 (End)
%e A202201 Some solutions for n=1:
%e A202201 ..1..0..0..0..0..0..0..0..0....1..1..1..1..1..1..1..0..0
%e A202201 ..1..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1..1
%e A202201 ..1..1..1..1..0..0..0..0..0....1..1..1..1..0..0..0..0..0
%Y A202201 Cf. A202202.
%K A202201 nonn
%O A202201 1,1
%A A202201 _R. H. Hardin_, Dec 14 2011