A196584 - OEIS

%I #8 Feb 22 2018 10:55:51

%S 1,7,20,65,203,648,2057,6527,20740,65833,209091,663912,2108281,

%T 6694767,21258988,67507481,214367707,680719048,2161603009,6864108879,

%U 21796779780,69215046289,219790389515,697938050920,2216282199881,7037740324047

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,2,0,1,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 3's, every 1 is next to 1 2's, every 2 is next to 2 0's, every 3 is next to 3 1's, every 4 is next to 4 4's.

%C Column 2 of A196590.

%H R. H. Hardin, <a href="/A196584/b196584.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -3*a(n-4) -a(n-5) -2*a(n-6) -a(n-7).

%F Empirical g.f.: x*(1 + 6*x + 7*x^2 - x^3 - 7*x^4 - 3*x^5) / (1 - x - 6*x^2 - 4*x^3 + 3*x^4 + x^5 + 2*x^6 + x^7). - _Colin Barker_, Feb 22 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A196590.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 04 2011