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A231338 Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order. 1

%I #8 Sep 28 2018 15:19:09

%S 4,9,22,59,159,439,1236,3527,10184,29679,87109,257077,761860,2264909,

%T 6749138,20146867,60218835,180167387,539423380,1615890811,4842424660,

%U 14515699655,43521570985,130508409225,391401045892,1173929246129

%N Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.

%H R. H. Hardin, <a href="/A231338/b231338.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) - 8*a(n-4) + 6*a(n-5) - a(n-6) + 3*a(n-7).

%F Empirical g.f.: x*(4 - 11*x + x^2 - 5*x^3 + 10*x^4 + 2*x^5 + 3*x^6) / ((1 - x)*(1 - 3*x)*(1 + x + x^2)*(1 - 2*x - x^3)). - _Colin Barker_, Sep 28 2018

%e Some solutions for n=6:

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

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

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

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

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

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

%e ..1..1..2....0..0..0....1..1..0....1..2..2....3..3..3....2..2..2....0..0..0

%Y Column 2 of A231343.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2013

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)