A251251 - OEIS

%I #10 Nov 27 2018 09:07:51

%S 8,18,38,84,180,394,850,1852,4008,8714,18886,41020,88964,193138,

%T 419010,909460,1973352,4282722,9293318,20168132,43765364,94976442,

%U 206104402,447268364,970605128,2106305818,4570852838,9919165164,21525417860

%N Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock having a single 1 or two 1s on the same edge.

%H R. H. Hardin, <a href="/A251251/b251251.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x*(4 + 5*x - 2*x^2) / (1 - x - 3*x^2 + x^3). - _Colin Barker_, Nov 27 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251258.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014