A210302 - OEIS

%I #9 Jul 15 2018 06:53:38

%S 0,29,414,4553,45890,446093,4266246,40490097,382887722,3614390197,

%T 34090440494,321405533785,3029622853138,28555016231773,

%U 269126357016278,2536415298825665,23904507782220922,225287438517410949

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

%C Column 1 of A210309.

%H R. H. Hardin, <a href="/A210302/b210302.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 15*a(n-1) - 57*a(n-2) + 41*a(n-3) + 10*a(n-4) - 8*a(n-5).

%F Empirical g.f.: x^2*(29 - 21*x - 4*x^2 + 4*x^3) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 9*x - 4*x^2)). - _Colin Barker_, Jul 15 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A210309.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 19 2012