cp's OEIS Frontend

A221568 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.

%I A221568 #13 Jan 31 2017 10:51:42
%S A221568 0,10,26,100,342,1210,4240,14898,52306,183684,645006,2264978,7953568,
%T A221568 27929338,98075178,344395620,1209361446,4246729738,14912591664,
%U A221568 52366268642,183886620962,645726538244,2267499179678,7962430263202,27960449231680,98184435580010
%N A221568 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.
%C A221568 Column 3 of A221573.
%H A221568 R. H. Hardin, <a href="/A221568/b221568.txt">Table of n, a(n) for n = 1..210</a>
%H A221568 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 A221568 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-1,1).
%F A221568 a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4).
%F A221568 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 A221568 Some solutions for n=6
%e A221568 ..1....0....1....0....3....0....3....2....0....0....3....0....0....0....2....0
%e A221568 ..3....2....1....2....1....2....3....0....2....2....1....0....0....3....2....0
%e A221568 ..2....2....1....3....0....0....0....3....3....3....2....0....0....2....0....0
%e A221568 ..2....2....1....3....3....1....3....3....0....0....0....3....3....2....1....2
%e A221568 ..3....3....1....3....1....3....3....2....0....1....1....0....3....0....1....2
%e A221568 ..0....0....1....3....1....3....3....2....2....1....1....3....3....0....3....2
%o A221568 (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 A221568 nonn,easy
%O A221568 1,2
%A A221568 _R. H. Hardin_, Jan 20 2013