A231765 - OEIS

%I #8 Oct 01 2018 06:28:07

%S 9,33,100,315,961,3024,9409,29319,91204,284279,885481,2758192,8590761,

%T 26760591,83356900,259648623,808776721,2519272112,7847302225,

%U 24443615655,76139572356,237167776135,738755721081,2301155717168,7167887098681

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

%H R. H. Hardin, <a href="/A231765/b231765.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-3) + 7*a(n-4) - 20*a(n-5) - 2*a(n-6) - 4*a(n-8) + 8*a(n-9).

%F Empirical g.f.: x*(9 + 6*x + x^2 + 6*x^3 - 80*x^4 - 10*x^5 - 8*x^7 + 32*x^8) / ((1 - 3*x - x^2 + 2*x^3)*(1 + x^2 - 6*x^4 - 4*x^6)). - _Colin Barker_, Oct 01 2018

%e Some solutions for n=7:

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

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

%Y Row 1 of A231764.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2013