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Number of n X 3 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
1

%I #7 Oct 01 2018 21:10:18

%S 9,66,852,11517,156913,2125749,28852936,391447970,5311170384,

%T 72061691152,977727048997,13265735926493,179988561188366,

%U 2442072186590951,33133863936280024,449557939142907661,6099570552966630306

%N Number of n X 3 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

%H R. H. Hardin, <a href="/A232018/b232018.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) + 59*a(n-2) + 62*a(n-3) - 275*a(n-4) - 257*a(n-5) + 146*a(n-6) + 84*a(n-7) for n>8.

%F Empirical g.f.: x*(9 - 15*x - 273*x^2 - 603*x^3 + 1375*x^4 + 1668*x^5 - 778*x^6 - 504*x^7) / (1 - 9*x - 59*x^2 - 62*x^3 + 275*x^4 + 257*x^5 - 146*x^6 - 84*x^7). - _Colin Barker_, Oct 01 2018

%e Some solutions for n=5:

%e ..1..1..1....0..0..0....2..0..0....2..0..0....1..1..1....1..1..0....0..0..2

%e ..0..0..0....1..0..0....0..0..0....0..2..2....0..0..0....1..0..2....0..0..1

%e ..0..0..0....0..0..0....1..2..1....0..0..1....0..2..1....0..0..2....0..2..2

%e ..2..0..1....0..2..0....1..1..0....0..0..0....0..0..0....0..0..0....2..1..1

%e ..0..0..0....0..0..0....0..0..2....2..0..0....1..0..0....1..0..0....1..1..2

%Y Column 3 of A232023.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 17 2013