A205829 - OEIS

A205829

Number of (n+1) X 2 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to two.

%I #9 Jun 12 2018 11:36:51

%S 30,111,423,1611,6132,23340,88839,338148,1287093,4899063,18647307,

%T 70977258,270160788,1028313201,3914069274,14898124683,56706742659,

%U 215842915227,821563042932,3127115999160,11902743868935,45305422519512

%N Number of (n+1) X 2 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to two.

%C Column 1 of A205836.

%H R. H. Hardin, <a href="/A205829/b205829.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 3*x*(10 - 3*x + 3*x^2) / (1 - 4*x + x^2 - x^3). - _Colin Barker_, Jun 12 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A205836.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2012