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 A212836 #10 Jul 21 2018 10:07:09 %S A212836 2,17,50,107,194,317,482,695,962,1289,1682,2147,2690,3317,4034,4847, %T A212836 5762,6785,7922,9179,10562,12077,13730,15527,17474,19577,21842,24275, %U A212836 26882,29669,32642,35807,39170,42737,46514,50507,54722,59165,63842,68759,73922 %N A212836 Number of 0..n arrays of length 3 with 0 never adjacent to n. %C A212836 Row 2 of A212835. %H A212836 R. H. Hardin, <a href="/A212836/b212836.txt">Table of n, a(n) for n = 1..210</a> %F A212836 Empirical: a(n) = n^3 + 3*n^2 - n - 1. %F A212836 Conjectures from _Colin Barker_, Jul 21 2018: (Start) %F A212836 G.f.: x*(2 + 9*x - 6*x^2 + x^3) / (1 - x)^4. %F A212836 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. %F A212836 (End) %e A212836 Some solutions for n=5: %e A212836 ..4....1....2....5....0....3....4....2....4....0....2....5....4....3....1....1 %e A212836 ..4....2....4....1....3....5....2....1....3....0....4....4....4....2....3....2 %e A212836 ..2....1....3....5....3....1....4....4....5....3....2....3....1....2....0....0 %Y A212836 Cf. A212835. %K A212836 nonn %O A212836 1,1 %A A212836 _R. H. Hardin_, May 28 2012