A231799 - OEIS

%I #8 Oct 01 2018 06:27:54

%S 5,13,32,79,200,500,1249,3133,7845,19640,49195,123202,308530,772687,

%T 1935097,4846171,12136616,30394575,76119168,190630456,477408937,

%U 1195607773,2994242313,7498685908,18779471815,47030715498,117782237374

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

%H R. H. Hardin, <a href="/A231799/b231799.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(5 + 8*x + 9*x^2 - 4*x^3 - 8*x^4 - 8*x^5) / (1 - x - 2*x^2 - 5*x^3 + 2*x^5 + 4*x^6). - _Colin Barker_, Oct 01 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

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

%Y Column 1 of A231806.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2013