A202529 - OEIS

%I #8 Jun 01 2018 09:36:33

%S 1940,4901,10240,21297,46621,100550,214388,460948,992061,2128796,

%T 4570909,9821889,21095902,45306296,97317908,209034085,448973976,

%U 964350281,2071342213,4449024294,9556039324,20525432468,44086562621,94693444852

%N Number of (n+2) X 7 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

%C Column 5 of A202532.

%H R. H. Hardin, <a href="/A202529/b202529.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>8.

%F Empirical g.f.: x*(1940 + 1021*x + 438*x^2 - 3063*x^3 - 1895*x^4 + 510*x^5 + 976*x^6 + 64*x^7) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A202532.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2011