A221568 - OEIS

%I #13 Jan 31 2017 10:51:42

%S 0,10,26,100,342,1210,4240,14898,52306,183684,645006,2264978,7953568,

%T 27929338,98075178,344395620,1209361446,4246729738,14912591664,

%U 52366268642,183886620962,645726538244,2267499179678,7962430263202,27960449231680,98184435580010

%N Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.

%C Column 3 of A221573.

%H R. H. Hardin, <a href="/A221568/b221568.txt">Table of n, a(n) for n = 1..210</a>

%H Sergey Kitaev, Jeffrey Remmel, <a href="http://arxiv.org/abs/1304.4286">(a,b)-rectangle patterns in permutations and words</a>, arXiv:1304.4286 [math.CO], 2013.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-1,1).

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

%F G.f.: 2*x^2*(5 - 2*x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - _Colin Barker_, Jan 31 2017

%e Some solutions for n=6

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

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

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

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

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

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

%o (PARI) concat(0, Vec(2*x^2*(5 - 2*x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)) + O(x^30))) \\ _Colin Barker_, Jan 31 2017

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, Jan 20 2013