Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Oct 19 2017 06:54:11
%S 0,2,5,26,100,418,1692,6932,28288,115604,472188,1929012,7880012,
%T 32190588,131500508,537189116,2194454252,8964498844,36620598988,
%U 149597691420,611116954220,2496455194876,10198192807820,41660325742812
%N 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 Column 4 of A221683.
%H R. H. Hardin, <a href="/A221679/b221679.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).
%F 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 Some solutions for n=6
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....0....0....0....0....1....1....1....1....0....0....0....1....0....1....1
%e ..0....2....1....0....3....3....0....1....4....4....1....4....3....3....3....2
%e ..2....2....2....3....4....2....2....0....4....3....2....4....2....3....3....4
%e ..2....4....4....2....4....0....3....3....2....0....1....2....0....0....2....4
%e ..2....4....3....2....3....0....2....2....3....1....1....2....1....1....1....3
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 22 2013