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Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having one or two distinct values, and new values 0..3 introduced in row major order.
1

%I #9 Jul 14 2018 05:19:49

%S 0,0,9,162,1845,17262,144945,1138194,8548029,62230230,442977705,

%T 3101305338,21442016565,146833223166,998073454689,6745063632354,

%U 45376569607725,304167049525926,2033050559738265,13557845469637962

%N Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having one or two distinct values, and new values 0..3 introduced in row major order.

%C Column 1 of A209969.

%H R. H. Hardin, <a href="/A209962/b209962.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 83*a(n-2) + 132*a(n-3) + 56*a(n-4) - 88*a(n-5) - 32*a(n-6).

%F Empirical g.f.: 9*x^2*(1 + 2*x) / ((1 - x)*(1 - 4*x)*(1 - 5*x - 2*x^2)*(1 - 6*x - 4*x^2)). - _Colin Barker_, Jul 14 2018

%e All solutions for n=4:

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

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

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

%e ..2..2....2..3....2..2....2..2....2..2....2..2....2..2....2..2....2..2

%e ..2..3....2..2....3..3....3..2....2..3....2..3....2..3....2..3....2..3

%Y Cf. A209969.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 16 2012