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 A212840 #9 Jul 21 2018 10:06:45 %S A212840 2,577,8042,49835,204994,654797,1758602,4159927,8927810,17738489, %T A212840 33102442,58641827,99423362,162351685,256628234,394280687,590768002, %U A212840 865666097,1243439210,1754301979,2435177282,3330754877,4494655882 %N A212840 Number of 0..n arrays of length 7 with 0 never adjacent to n. %C A212840 Row 6 of A212835. %H A212840 R. H. Hardin, <a href="/A212840/b212840.txt">Table of n, a(n) for n = 1..210</a> %F A212840 Empirical: a(n) = n^7 + 7*n^6 + 9*n^5 - 15*n^4 - 13*n^3 + 15*n^2 - 1*n - 1. %F A212840 Conjectures from _Colin Barker_, Jul 21 2018: (Start) %F A212840 G.f.: x*(2 + 561*x + 3482*x^2 + 1543*x^3 - 682*x^4 + 151*x^5 - 18*x^6 + x^7) / (1 - x)^8. %F A212840 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8. %F A212840 (End) %e A212840 Some solutions for n=5: %e A212840 ..3....3....1....3....0....0....1....1....0....1....3....0....3....3....1....0 %e A212840 ..5....1....4....4....0....3....1....3....3....2....5....3....5....3....0....1 %e A212840 ..3....0....0....4....1....4....2....3....2....2....1....0....4....1....0....5 %e A212840 ..3....4....0....3....4....4....4....0....0....3....2....1....5....3....2....1 %e A212840 ..0....3....1....1....0....1....2....0....2....4....4....1....3....0....0....5 %e A212840 ..1....1....2....3....2....5....1....0....3....1....5....4....3....3....4....2 %e A212840 ..3....3....1....1....3....3....5....2....4....0....2....1....2....4....4....2 %Y A212840 Cf. A212835. %K A212840 nonn %O A212840 1,1 %A A212840 _R. H. Hardin_, May 28 2012