A198287 - OEIS

%I #9 Mar 02 2018 06:27:04

%S 2,17,272,4667,80702,1397477,24207692,419373647,7265397242,

%T 125869473977,2180631250952,37778460128867,654494991508022,

%U 11338834542738317,196440265628093252,3403240245856247927,58959623892961901042

%N Number of 2n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor.

%C Column 1 of A198290.

%H R. H. Hardin, <a href="/A198287/b198287.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 23*a(n-1) - 103*a(n-2) + 81*a(n-3).

%F Conjectures from _Colin Barker_, Mar 02 2018: (Start)

%F G.f.: x*(2 - 29*x + 87*x^2) / ((1 - x)*(1 - 22*x + 81*x^2)).

%F a(n) = (216 - (11-2*sqrt(10))^n*(-8+sqrt(10)) + (8+sqrt(10))*(11+2*sqrt(10))^n) / 216.

%F (End)

%e Some solutions for n=2:

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

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

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

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

%Y Cf. A198290.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 23 2011