A205730 - OEIS

A205730

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

%I #9 Dec 10 2015 02:09:42

%S 369,978,3318,9198,34674,97380,370008,1053624,4060848,11593452,

%T 44691564,127862298,493245942,1412611194,5445496374,15610049862,

%U 60135842922,172528522548,664117714260,1906895501304,7334482622244,21076547401356

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

%C Column 2 of A205736.

%H R. H. Hardin, <a href="/A205730/b205730.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +11*a(n-2) -9*a(n-3) +8*a(n-4) -26*a(n-5) -99*a(n-6) +51*a(n-7) +135*a(n-8) +25*a(n-9) -54*a(n-10) -42*a(n-11) for n>14.

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 30 2012