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Number of n X 3 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
1

%I #6 Sep 21 2018 21:48:05

%S 1,2,3,7,16,43,117,330,935,2667,7616,21775,62273,178130,509563,

%T 1457727,4170224,11930147,34129757,97638522,279324735,799093699,

%U 2286051744,6539949991,18709526921,53524323778,153122698291,438054310967

%N Number of n X 3 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

%H R. H. Hardin, <a href="/A301902/b301902.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=5

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

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

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

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

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

%Y Column 3 of A301906.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 28 2018