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 A212838 #10 Jul 21 2018 10:07:24 %S A212838 2,99,634,2309,6306,14407,29114,53769,92674,151211,235962,354829, %T A212838 517154,733839,1017466,1382417,1844994,2423539,3138554,4012821, %U A212838 5071522,6342359,7855674,9644569,11745026,14196027,17039674,20321309,24089634,28396831 %N A212838 Number of 0..n arrays of length 5 with 0 never adjacent to n. %C A212838 Row 4 of A212835. %H A212838 R. H. Hardin, <a href="/A212838/b212838.txt">Table of n, a(n) for n = 1..210</a> %F A212838 Empirical: a(n) = n^5 + 5*n^4 + 2*n^3 - 8*n^2 + n + 1. %F A212838 Conjectures from _Colin Barker_, Jul 21 2018: (Start) %F A212838 G.f.: x*(2 + 87*x + 70*x^2 - 50*x^3 + 12*x^4 - x^5) / (1 - x)^6. %F A212838 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. %F A212838 (End) %e A212838 Some solutions for n=5: %e A212838 ..5....5....3....3....1....2....5....5....4....0....5....5....0....1....2....2 %e A212838 ..4....2....3....2....4....2....1....5....1....2....3....3....3....2....2....4 %e A212838 ..5....3....5....0....3....1....3....4....5....5....1....1....1....4....1....0 %e A212838 ..2....1....4....2....0....2....4....3....3....3....5....3....5....1....5....4 %e A212838 ..4....5....1....4....1....0....4....4....2....4....5....1....3....0....2....0 %Y A212838 Cf. A212835. %K A212838 nonn %O A212838 1,1 %A A212838 _R. H. Hardin_, May 28 2012