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Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.
1

%I #8 Feb 22 2019 05:49:59

%S 8,61,409,2837,19776,137459,955680,6645662,46211001,321328965,

%T 2234376733,15536845232,108036163039,751234447860,5223743482218,

%U 36323541679065,252577425569649,1756308801126965,12212574412144160,84920700547463563

%N Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.

%H R. H. Hardin, <a href="/A283852/b283852.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 2*a(n-2) + 19*a(n-3) - 50*a(n-4) - 2*a(n-5) - 48*a(n-6) + 88*a(n-7) - 32*a(n-8).

%F Empirical g.f.: x*(8 + 5*x - 2*x^2 - 56*x^3 - 24*x^4 - 4*x^5 + 72*x^6 - 32*x^7) / (1 - 7*x + 2*x^2 - 19*x^3 + 50*x^4 + 2*x^5 + 48*x^6 - 88*x^7 + 32*x^8). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A283857.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 17 2017