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A238649 Number of (n+2) X (3+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order. 1

%I #7 Oct 24 2018 08:57:21

%S 3,18,51,189,630,2187,7473,25692,88119,302511,1038144,3563151,

%T 12228903,41971050,144048471,494389041,1696791534,5823557223,

%U 19987023645,68597444364,235433215419,808030095435,2773239244320,9518031521451

%N Number of (n+2) X (3+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order.

%H R. H. Hardin, <a href="/A238649/b238649.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 3*x*(1 + 4*x - x^3) / (1 - 2*x - 5*x^2 + x^4). - _Colin Barker_, Oct 24 2018

%e Some solutions for n=5:

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

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

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

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

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

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

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

%Y Column 3 of A238654.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2014

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)