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Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
1

%I #8 Feb 11 2019 14:23:22

%S 4,5,11,22,47,102,224,494,1089,2400,5289,11661,25718,56728,125125,

%T 275973,608663,1342423,2960792,6530255,14402991,31766847,70063951,

%U 154530760,340828154,751720173,1657971361,3656771426,8065263401,17788497730

%N Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279710/b279710.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(4 - 7*x + 4*x^2 + 3*x^3 - 8*x^4 - 5*x^6) / ((1 - x)*(1 + x)*(1 - 2*x - x^3)*(1 - x + x^2 + x^3)). - _Colin Barker_, Feb 11 2019

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A279709.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2016