cp's OEIS Frontend

A221679 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%I A221679 #9 Oct 19 2017 06:54:11
%S A221679 0,2,5,26,100,418,1692,6932,28288,115604,472188,1929012,7880012,
%T A221679 32190588,131500508,537189116,2194454252,8964498844,36620598988,
%U A221679 149597691420,611116954220,2496455194876,10198192807820,41660325742812
%N A221679 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
%C A221679 Column 4 of A221683.
%H A221679 R. H. Hardin, <a href="/A221679/b221679.txt">Table of n, a(n) for n = 1..210</a>
%F A221679 Empirical: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).
%F A221679 Empirical g.f.: x^2*(2 - x + 3*x^2 + 2*x^3 + 2*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - _Colin Barker_, Oct 19 2017
%e A221679 Some solutions for n=6
%e A221679 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221679 ..1....0....0....0....0....1....1....1....1....0....0....0....1....0....1....1
%e A221679 ..0....2....1....0....3....3....0....1....4....4....1....4....3....3....3....2
%e A221679 ..2....2....2....3....4....2....2....0....4....3....2....4....2....3....3....4
%e A221679 ..2....4....4....2....4....0....3....3....2....0....1....2....0....0....2....4
%e A221679 ..2....4....3....2....3....0....2....2....3....1....1....2....1....1....1....3
%K A221679 nonn
%O A221679 1,2
%A A221679 _R. H. Hardin_, Jan 22 2013