A183702 - OEIS

%I #9 Apr 04 2018 10:09:07

%S 192,2472,31800,409128,5263608,67718760,871232952,11208812712,

%T 144206530680,1855283342568,23869073504568,307086608771880,

%U 3950810460600312,50828993677128552,653938381502821560

%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock nonsingular.

%C Column 1 of A183710.

%H R. H. Hardin, <a href="/A183702/b183702.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 11*a(n-1) + 24*a(n-2).

%F Conjectures from _Colin Barker_, Apr 04 2018: (Start)

%F G.f.: 24*x*(8 + 15*x) / (1 - 11*x - 24*x^2).

%F a(n) = (3*2^(-1-n)*((11-sqrt(217))^n*(-73+5*sqrt(217)) + (11+sqrt(217))^n*(73+5*sqrt(217)))) / sqrt(217).

%F (End)

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A183710.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011