cp's OEIS Frontend

A221680 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%I A221680 #9 Oct 19 2017 07:40:57
%S A221680 0,2,5,32,133,636,2856,13169,60120,275632,1261451,5777107,26449970,
%T A221680 121113272,554546205,2539172736,11626346343,53234805475,243751618738,
%U A221680 1116090939600,5110360772166,23399338403512,107140971422686
%N A221680 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
%C A221680 Column 5 of A221683.
%H A221680 R. H. Hardin, <a href="/A221680/b221680.txt">Table of n, a(n) for n = 1..210</a>
%F A221680 Empirical: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6).
%F A221680 Empirical g.f.: x^2*(2 - 3*x + 6*x^2 + 2*x^3) / (1 - 4*x - 3*x^2 + 6*x^3 - 19*x^4 - 5*x^5 - x^6). - _Colin Barker_, Oct 19 2017
%e A221680 Some solutions for n=6
%e A221680 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221680 ..0....0....0....0....0....0....1....0....0....0....1....0....1....1....0....0
%e A221680 ..5....1....4....3....3....1....2....4....1....1....2....1....1....1....0....4
%e A221680 ..4....3....4....3....2....2....3....5....1....2....3....1....2....1....0....4
%e A221680 ..5....3....2....0....1....3....2....2....1....0....5....1....3....1....1....3
%e A221680 ..5....3....2....1....1....4....1....2....0....1....4....1....2....1....0....4
%K A221680 nonn
%O A221680 1,2
%A A221680 _R. H. Hardin_, Jan 22 2013