cp's OEIS Frontend

A221538 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221538 #8 Oct 18 2017 18:23:00
%S A221538 0,4,14,68,303,1386,6311,28762,131012,596784,2718469,12383368,
%T A221538 56409683,256961576,1170529586,5332078812,24289062227,110643256974,
%U A221538 504010005519,2295902089838,10458455859448,47641099074536,217018109737881
%N A221538 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221538 Column 4 of A221542.
%H A221538 R. H. Hardin, <a href="/A221538/b221538.txt">Table of n, a(n) for n = 1..210</a>
%F A221538 Empirical: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6.
%F A221538 Empirical g.f.: x^2*(4 - 6*x + 10*x^2 + x^3 + x^4) / (1 - 5*x + 3*x^2 - x^3 - 15*x^4 - 3*x^5). - _Colin Barker_, Oct 18 2017
%e A221538 Some solutions for n=6
%e A221538 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221538 ..4....3....4....3....2....4....4....2....3....4....3....2....4....4....4....0
%e A221538 ..3....3....0....4....4....3....0....1....3....0....2....2....0....0....0....2
%e A221538 ..3....1....2....4....4....0....3....1....2....1....2....0....3....1....0....4
%e A221538 ..0....4....2....3....1....4....3....1....2....3....4....0....3....4....4....4
%e A221538 ..3....2....2....3....3....1....3....4....2....1....0....3....1....2....2....0
%K A221538 nonn
%O A221538 1,2
%A A221538 _R. H. Hardin_, Jan 19 2013