A183690 - OEIS

%I #9 Apr 04 2018 10:48:15

%S 50,314,1970,12362,77570,486746,3054290,19165418,120261410,754630394,

%T 4735243250,29713259402,186448243010,1169947290266,7341322395410,

%U 46066190299178,289061530659170,1813837175689274,11381678123719730

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

%C Column 1 of A183698.

%H R. H. Hardin, <a href="/A183690/b183690.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) + 8*a(n-2).

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

%F G.f.: 2*x*(25 + 32*x) / (1 - 5*x - 8*x^2).

%F a(n) = (2^(1-n)*((5-sqrt(57))^n*(-15+2*sqrt(57)) + (5+sqrt(57))^n*(15+2*sqrt(57)))) / sqrt(57).

%F (End)

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A183698.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011