A184679 - OEIS

%I #9 Apr 14 2018 08:21:36

%S 28,128,544,2384,10384,45392,198352,867152,3791056,16575056,72469456,

%T 316854608,1385372368,6057228368,26483886544,115794964304,

%U 506288081104,2213633766992,9678629263312,42317689343312,185024841512656

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

%C Column 2 of A184686.

%H R. H. Hardin, <a href="/A184679/b184679.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) - 12*a(n-3).

%F Conjectures from _Colin Barker_, Apr 14 2018: (Start)

%F G.f.: 4*x*(7 - 3*x - 24*x^2) / ((1 - 2*x)*(1 - 3*x - 6*x^2)).

%F a(n) = 2^(-2-n)*(11*2^(1+2*n) - 3*(3-sqrt(33))^n*(-55+7*sqrt(33)) + 3*(3+sqrt(33))^n*(55+7*sqrt(33))) / 11.

%F (End)

%e Some solutions for 5 X 3:

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

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

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

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

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

%Y Cf. A184686.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 19 2011