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Number of nX2 0..1 arrays with every element unequal to 0, 1 or 3 king-move adjacent elements, with upper left element zero.
4

%I #4 Apr 28 2018 09:19:58

%S 2,5,7,17,31,49,103,193,327,641,1207,2129,4039,7585,13687,25585,47847,

%T 87425,162391,302609,556615,1031329,1916983,3538225,6550311,12155585,

%U 22474519,41599313,77121031,142707937,264156151,489441649,906031335

%N Number of nX2 0..1 arrays with every element unequal to 0, 1 or 3 king-move adjacent elements, with upper left element zero.

%C Column 2 of A303682.

%H R. H. Hardin, <a href="/A303677/b303677.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A303682.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 28 2018