cp's OEIS Frontend

A221537 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221537 #8 Oct 18 2017 18:22:46
%S A221537 0,3,8,30,103,364,1276,4483,15740,55274,194095,681576,2393384,8404483,
%T A221537 29512736,103635366,363920471,1277923892,4487489988,15758032643,
%U A221537 55335074484,194311722642,682334774239,2396050726160,8413845078800
%N A221537 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221537 Column 3 of A221542.
%H A221537 R. H. Hardin, <a href="/A221537/b221537.txt">Table of n, a(n) for n = 1..210</a>
%F A221537 Empirical: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4).
%F A221537 Empirical g.f.: x^2*(3 - x) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - _Colin Barker_, Oct 18 2017
%e A221537 Some solutions for n=6
%e A221537 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221537 ..3....0....3....2....0....0....2....0....0....0....0....2....0....2....0....3
%e A221537 ..3....0....1....2....0....0....2....2....3....3....1....2....3....2....0....3
%e A221537 ..0....3....3....2....2....3....0....2....3....0....3....0....3....0....0....0
%e A221537 ..1....1....3....0....1....3....0....2....3....0....3....1....1....1....0....0
%e A221537 ..1....1....0....3....1....1....3....0....3....3....0....3....1....1....0....2
%K A221537 nonn
%O A221537 1,2
%A A221537 _R. H. Hardin_, Jan 19 2013