A221519 - OEIS

%I #10 Oct 18 2017 13:28:40

%S 0,6,10,36,94,274,768,2182,6170,17476,49470,140066,396544,1122694,

%T 3178538,8999012,25477790,72132146,204218880,578179846,1636929594,

%U 4634437764,13120914558,37147634242,105171535360,297759253766

%N Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more.

%C Column 3 of A221524.

%H R. H. Hardin, <a href="/A221519/b221519.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x^2*(3 + 2*x + x^2) / ((1 + x)*(1 - 2*x - 2*x^2 - x^3)). - _Colin Barker_, Oct 18 2017

%e Some solutions for n=6

%e ..0....2....0....2....3....0....0....3....3....2....0....1....3....1....3....1

%e ..3....0....3....0....0....2....3....1....0....0....2....3....0....3....1....3

%e ..0....0....0....2....1....1....1....3....0....2....3....2....1....0....1....2

%e ..1....3....3....3....3....3....3....2....2....0....0....0....3....1....3....0

%e ..3....3....2....0....3....2....3....0....3....2....0....3....0....3....0....3

%e ..1....1....0....3....0....0....1....3....1....0....3....1....3....1....3....0

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013