A210006 - OEIS

%I #9 Jul 14 2018 05:21:09

%S 88,2691,70923,1808865,45763485,1155440875,29157605895,735696878225,

%T 18562285346341,468338954286595,11816481504639071,298136973245043705,

%U 7522175051206144237,189788991513097693371,4788490127902930108215

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

%C Column 2 of A210012.

%H R. H. Hardin, <a href="/A210006/b210006.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 30*a(n-1) - 109*a(n-2) - 290*a(n-3) + 96*a(n-4) + 136*a(n-5) - 48*a(n-6).

%F Empirical g.f.: x*(88 + 51*x - 215*x^2 + 14*x^3 + 84*x^4 - 24*x^5) / ((1 - 6*x - 3*x^2 + 2*x^3)*(1 - 24*x - 32*x^2 + 24*x^3)). - _Colin Barker_, Jul 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A210012.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 16 2012