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Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
1

%I #7 Feb 15 2018 12:04:15

%S 3,3,5,11,19,35,65,120,220,404,744,1369,2517,4629,8515,15662,28806,

%T 52982,97450,179239,329671,606359,1115269,2051300,3772928,6939496,

%U 12763724,23476149,43179369,79419241,146074759,268673370,494167370,908915498

%N Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A299595.

%H R. H. Hardin, <a href="/A299590/b299590.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(3 + 2*x^2 - x^4 + x^7) / ((1 + x^2)*(1 - x - x^2 - x^3)). - _Colin Barker_, Feb 15 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A299595.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2018