This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A221593 #9 Oct 19 2017 06:11:35 %S A221593 0,16,44,256,1068,5082,22912,105586,482204,2210256,10115926,46327024, %T A221593 212107056,971225210,4446995942,20362020404,93233503292,426898240022, %U A221593 1954682503544,8950108307086,40980784959354,187642965834692 %N A221593 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less. %C A221593 Column 5 of A221596. %H A221593 R. H. Hardin, <a href="/A221593/b221593.txt">Table of n, a(n) for n = 1..210</a> %F A221593 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 A221593 Empirical g.f.: 2*x^2*(8 - 10*x + 16*x^2 + 4*x^3 + x^4) / (1 - 4*x - 3*x^2 + 6*x^3 - 19*x^4 - 5*x^5 - x^6). - _Colin Barker_, Oct 19 2017 %e A221593 Some solutions for n=6 %e A221593 ..2....4....0....0....3....5....2....1....2....4....5....4....2....2....1....3 %e A221593 ..2....3....1....0....3....4....1....0....3....3....5....3....2....1....1....4 %e A221593 ..4....0....5....3....1....2....2....0....2....5....1....2....3....4....2....5 %e A221593 ..4....0....5....4....2....2....2....2....4....4....1....5....1....4....3....5 %e A221593 ..1....4....3....4....3....0....1....3....5....1....1....5....1....4....2....1 %e A221593 ..2....5....2....5....3....1....1....3....4....0....2....5....0....4....3....0 %K A221593 nonn %O A221593 1,2 %A A221593 _R. H. Hardin_, Jan 20 2013