A206233 - OEIS

A206233

Number of (n+1) X 4 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

%I #8 Jun 14 2018 09:19:33

%S 310,1136,4456,27168,133392,607008,3503136,17206032,78302496,

%T 451903008,2219576592,10101020448,58295486496,286325378832,

%U 1303031636256,7520117756448,36935973867792,168091081075488,970095190580256

%N Number of (n+1) X 4 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

%C Column 3 of A206238.

%H R. H. Hardin, <a href="/A206233/b206233.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 129*a(n-3) - 129*a(n-4) for n>7.

%F Empirical g.f.: 2*x*(155 + 413*x + 1660*x^2 - 8639*x^3 - 165*x^4 + 22668*x^5 - 16860*x^6) / ((1 - x)*(1 - 129*x^3)). - _Colin Barker_, Jun 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A206238.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2012