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Number of (n+1) X (1+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to one.
1

%I #8 Sep 30 2018 20:23:10

%S 5,17,42,121,351,978,2768,7851,22168,62688,177333,501398,1417871,

%T 4009693,11338691,32064185,90673442,256411571,725096165,2050472356,

%U 5798450868,16397214669,46369052496,131125251872,370804035439,1048582421408

%N Number of (n+1) X (1+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to one.

%H R. H. Hardin, <a href="/A231703/b231703.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) + 4*a(n-3) - 8*a(n-4) + 3*a(n-5) - 3*a(n-6) + 3*a(n-7) - 2*a(n-8) + a(n-9).

%F Empirical g.f.: x*(5 + 2*x - 4*x^2 - 8*x^3 + 2*x^4 - x^5 + x^6 - x^7 + x^8) / (1 - 3*x + x^2 - 4*x^3 + 8*x^4 - 3*x^5 + 3*x^6 - 3*x^7 + 2*x^8 - x^9). - _Colin Barker_, Sep 30 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

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

%Y Column 1 of A231710.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 12 2013