A186055 - OEIS

%I #8 Apr 17 2018 08:33:45

%S 87,267,792,2328,6915,20475,60588,179442,531306,1573062,4657767,

%T 13791129,40833855,120904779,357985743,1059956097,3138413982,

%U 9292498818,27514066965,81466129305,241212255042,714202974702,2114676514230

%N Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having a positive determinant.

%C Column 1 of A186063.

%H R. H. Hardin, <a href="/A186055/b186055.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + 6*a(n-3) - 2*a(n-4) + 2*a(n-5) - 3*a(n-6) + 2*a(n-7).

%F Empirical g.f.: 3*x*(29 + 31*x + 57*x^2 - 15*x^3 + 13*x^4 - 25*x^5 + 22*x^6) / (1 - 2*x - x^2 - 6*x^3 + 2*x^4 - 2*x^5 + 3*x^6 - 2*x^7). - _Colin Barker_, Apr 17 2018

%e Some solutions for 4 X 3:

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

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

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

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

%Y Cf. A186063.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 11 2011