A202051 - OEIS

%I #11 May 26 2018 08:45:26

%S 1926,7848,25650,71964,180054,411696,874998,1750140,3325410,6046344,

%T 10581246,17906868,29418570,47069856,73546794,112483476,168725358,

%U 248648040,360539802,515057004,725762286,1009756368,1388415150

%N Number of (n+2) X 9 binary arrays avoiding patterns 001 and 110 in rows and columns.

%C Column 7 of A202052.

%H R. H. Hardin, <a href="/A202051/b202051.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/10080)*n^9 + (3/560)*n^8 + (211/1680)*n^7 + (67/40)*n^6 + (6709/480)*n^5 + (6041/80)*n^4 + (663941/2520)*n^3 + (79913/140)*n^2 + (4735/7)*n + 324.

%F Conjectures from _Colin Barker_, May 26 2018: (Start)

%F G.f.: 18*x*(107 - 634*x + 1880*x^2 - 3472*x^3 + 4298*x^4 - 3652*x^5 + 2114*x^6 - 800*x^7 + 179*x^8 - 18*x^9) / (1 - x)^10.

%F 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 (End)

%e Some solutions for n=3:

%e   1 0 1 0 1 0 0 0 0        1 0 1 0 1 0 1 1 1

%e   0 1 0 1 0 1 0 1 0        0 1 0 1 0 1 0 0 0

%e   1 0 1 0 1 0 0 0 0        1 0 1 0 1 1 1 1 1

%e   0 1 0 0 0 0 0 0 0        1 0 1 1 1 1 1 1 1

%e   1 0 1 0 1 0 0 0 0        1 0 1 1 1 1 1 1 1

%Y Cf. A202052.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2011