A183774 - OEIS

%I #16 Apr 05 2016 23:40:09

%S 5,13,33,85,217,557,1425,3653,9353,23965,61377,157237,402745,1031693,

%T 2642673,6769445,17340137,44417917,113778465,291450133,746563993,

%U 1912364525,4898620497,12548078597,32142560585,82334874973,210905117313

%N Half the number of (n+1)X2 binary arrays with no 2X2 subblock having exactly 2 ones

%C Column 1 of A183782.

%C a(n) appears to be sum of the elements of the n-th power of the matrix {{1, 2}, {2, 0}}. - _Griffin N. Macris_, Mar 25 2016

%H R. H. Hardin, <a href="/A183774/b183774.txt">Table of n, a(n) for n = 1..200</a>

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

%e Some solutions with a(1,1)=0 for 3X2

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2011