cp's OEIS Frontend

A221678 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%I A221678 #9 Oct 19 2017 06:15:16
%S A221678 0,2,5,20,68,241,844,2966,10413,36568,128408,450913,1583400,5560186,
%T A221678 19524853,68562444,240760252,845440977,2968805844,10425101678,
%U A221678 36608235997,128551546480,451414815600,1585164405441,5566379537040
%N A221678 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
%C A221678 Column 3 of A221683.
%H A221678 R. H. Hardin, <a href="/A221678/b221678.txt">Table of n, a(n) for n = 1..210</a>
%F A221678 Empirical: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4).
%F A221678 Empirical g.f.: x^2*(2 - x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - _Colin Barker_, Oct 19 2017
%e A221678 Some solutions for n=6
%e A221678 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221678 ..0....0....1....0....0....0....0....0....1....1....0....1....0....1....1....0
%e A221678 ..1....2....0....1....0....1....3....1....1....2....0....2....0....1....3....2
%e A221678 ..0....1....2....2....2....3....2....1....2....3....1....0....2....2....2....3
%e A221678 ..0....2....3....1....3....3....1....1....1....3....0....0....1....1....3....2
%e A221678 ..0....2....3....2....3....3....2....2....1....2....1....0....0....0....3....1
%K A221678 nonn
%O A221678 1,2
%A A221678 _R. H. Hardin_, Jan 22 2013