cp's OEIS Frontend

A221592 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less.

%I A221592 #15 Jan 31 2017 10:51:57
%S A221592 0,13,35,169,651,2715,11011,45099,184063,752155,3072247,12550859,
%T A221592 51270383,209444163,855592375,3495156539,14277953839,58326437619,
%U A221592 238267540647,973339457803,3976159254687,16242886662499,66353319815959,271057918757755,1107290419059023
%N A221592 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less.
%C A221592 Column 4 of A221596.
%H A221592 R. H. Hardin, <a href="/A221592/b221592.txt">Table of n, a(n) for n = 1..210</a>
%H A221592 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 A221592 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,4,0,6,4,4).
%F A221592 a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).
%F A221592 G.f.: x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - _Colin Barker_, Jan 31 2017
%e A221592 Some solutions for n=6
%e A221592 ..3....3....2....1....4....4....3....3....3....3....4....4....2....2....3....3
%e A221592 ..2....3....1....0....3....3....4....2....4....4....3....3....2....3....2....2
%e A221592 ..1....0....4....2....4....2....0....3....4....2....4....2....2....4....3....3
%e A221592 ..1....1....4....3....2....1....0....1....3....3....0....0....4....4....0....3
%e A221592 ..3....2....2....0....3....0....1....1....3....0....0....0....3....4....1....4
%e A221592 ..3....1....3....1....2....0....0....0....3....1....0....1....2....4....1....4
%o A221592 (PARI) concat(0, Vec(x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6) + O(x^30))) \\ _Colin Barker_, Jan 31 2017
%K A221592 nonn,easy
%O A221592 1,2
%A A221592 _R. H. Hardin_, Jan 20 2013