A206670 - OEIS

%I #7 Dec 13 2015 21:16:12

%S 360,1812,9318,47106,243432,1242930,6474150,33323136,173699544,

%T 898948062,4687777926,24335901672,126930698646,660162473754,

%U 3443416243986,17928893882562,93516332989608,487232601543270,2541312084390642

%N Number of (n+1) X 3 0..2 arrays with no 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors or the same number of counterclockwise edge increases as its vertical neighbors.

%C Column 2 of A206676.

%H R. H. Hardin, <a href="/A206670/b206670.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +22*a(n-2) -59*a(n-3) -112*a(n-4) -136*a(n-5) +525*a(n-6) +182*a(n-7) -684*a(n-8) +417*a(n-9) +136*a(n-10) +252*a(n-11) +514*a(n-12) +224*a(n-13) +52*a(n-14) -80*a(n-15) -48*a(n-16).

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 11 2012