A210089 - OEIS

A210089

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

%I #9 Jul 14 2018 05:56:22

%S 9,169,2370,29650,348621,3950131,43701168,475700584,5119557747,

%T 54648710593,579871850742,6125816087470,64500385137993,

%U 677459176188079,7102151283474060,74349727667778004,777498094039168623

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

%C Column 2 of A210095.

%H R. H. Hardin, <a href="/A210089/b210089.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) - 112*a(n-2) + 122*a(n-3) + 61*a(n-4) - 106*a(n-5) + 16*a(n-6).

%F Empirical g.f.: x*(9 - 11*x - 2*x^2 + 80*x^3 - 106*x^4 + 16*x^5) / ((1 - x)*(1 - 8*x)*(1 - 11*x + 5*x^2 + 11*x^3 - 2*x^4)). - _Colin Barker_, Jul 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A210095.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 17 2012