cp's OEIS Frontend

A221591 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less.

%I A221591 #18 Jan 31 2017 10:52:18
%S A221591 0,7,17,49,139,393,1113,3151,8921,25257,71507,202449,573169,1622743,
%T A221591 4594273,13007201,36825691,104260057,295178697,835703199,2366023849,
%U A221591 6698632793,18965016483,53693322401,152015310561,430382282407,1218488508337,3449756892049
%N A221591 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less.
%C A221591 Column 2 of A221596.
%H A221591 R. H. Hardin, <a href="/A221591/b221591.txt">Table of n, a(n) for n = 1..210</a>
%H A221591 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 A221591 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,1).
%F A221591 a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) for n>4.
%F A221591 G.f.: x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3). - _Colin Barker_, Jan 31 2017
%e A221591 Some solutions for n=6
%e A221591 ..2....1....1....0....1....1....0....1....1....2....2....2....1....1....2....1
%e A221591 ..2....1....2....0....2....0....1....1....0....2....2....1....1....1....1....1
%e A221591 ..2....2....1....1....2....2....1....0....0....0....0....2....1....0....2....1
%e A221591 ..1....2....0....0....2....1....0....1....2....1....1....2....0....2....0....2
%e A221591 ..0....1....1....0....0....2....2....0....2....0....0....1....1....1....1....1
%e A221591 ..0....2....2....1....0....2....1....0....1....0....1....2....1....1....0....2
%o A221591 (PARI) concat(0, Vec(x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + O(x^30))) \\ _Colin Barker_, Jan 31 2017
%K A221591 nonn,easy
%O A221591 1,2
%A A221591 _R. H. Hardin_, Jan 20 2013