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 A231295 Number of (n+1) X (1+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order. 1

%I #14 Sep 28 2018 09:53:29

%S 1,2,4,12,32,92,264,756,2176,6252,17976,51684,148592,427228,1228328,

%T 3531604,10153824,29193548,83935256,241324740,693839952,1994879932,

%U 5735538696,16490418228,47412092736,136315920428,391925964280

%N Number of (n+1) X (1+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order.

%H R. H. Hardin, <a href="/A231295/b231295.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + x)^2*(1 - 2*x) / ((1 - x)*(1 - x - 4*x^2 - 4*x^3)). - _Colin Barker_, Sep 28 2018

%e Some solutions for n=4:

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

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

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

%e ..1..1....1..1....0..0....2..2....1..1....0..1....1..2....1..0....1..1....0..0

%e ..1..1....1..1....0..0....2..2....1..1....1..1....2..2....0..0....1..1....0..0

%Y Column 1 of A231302.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 07 2013

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)