|
%I #8 May 14 2018 10:30:32
%S 3,13,71,433,2763,17941,117263,768313,5038611,33054493,216872663,
%T 1422982081,9336876123,61264171813,401987528351,2637661006153,
%U 17307148601763,113561761317421,745141474228583,4889285086978513
%N Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors.
%C Column 1 of A198452.
%H R. H. Hardin, <a href="/A198447/b198447.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 10*a(n-1) -25*a(n-2) +16*a(n-3).
%F Conjectures from _Colin Barker_, May 14 2018: (Start)
%F G.f.: x*(3 - 17*x + 16*x^2) / ((1 - x)*(1 - 9*x + 16*x^2)).
%F a(n) = 1/4 + (2^(-3-n)*((9+sqrt(17))^n*(-5+3*sqrt(17)) + (9-sqrt(17))^n*(5+3*sqrt(17)))) / sqrt(17).
%F (End)
%e Some solutions for n=3:
%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e ..1..0....1..2....2..0....1..2....2..2....2..0....2..2....2..0....2..2....2..0
%e ..1..0....1..2....2..0....1..2....1..1....2..0....1..1....2..0....1..1....2..0
%e ..2..2....2..0....0..2....2..1....0..2....1..1....2..2....0..1....2..2....1..2
%e ..1..1....2..0....0..2....2..1....0..2....2..2....1..1....0..1....0..0....1..2
%e ..2..0....0..2....2..1....0..2....1..0....1..0....2..0....2..0....1..2....0..1
%Y Cf. A198452.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 25 2011
| 