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 A221457 #7 Aug 05 2018 08:32:44 %S A221457 0,1,2,7,25,102,456,2218,11605,64647,379349,2320555,14658240,94843284, %T A221457 624544847,4164947151,28025750099,189783308469,1290899153376, %U A221457 8808076870934,60230644078721,412493027114619,2827998455493193 %N A221457 Number of 0..6 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..6 order. %C A221457 Column 6 of A221459. %H A221457 R. H. Hardin, <a href="/A221457/b221457.txt">Table of n, a(n) for n = 1..210</a> %F A221457 Empirical: a(n) = 16*a(n-1) - 79*a(n-2) + 70*a(n-3) + 361*a(n-4) - 372*a(n-5) - 964*a(n-6) + 144*a(n-7) + 1116*a(n-8) + 720*a(n-9) + 144*a(n-10). %F A221457 Empirical g.f.: x^2*(1 - 14*x + 54*x^2 + x^3 - 246*x^4 - 41*x^5 + 411*x^6 + 364*x^7 + 91*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 4*x - 4*x^2)*(1 - 6*x - 6*x^2)). - _Colin Barker_, Aug 05 2018 %e A221457 Some solutions for n=6: %e A221457 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 %e A221457 ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1 %e A221457 ..2....2....2....2....2....2....1....2....1....2....2....0....2....0....2....2 %e A221457 ..1....0....1....3....1....3....2....3....0....1....0....2....2....2....3....1 %e A221457 ..3....3....2....1....2....0....2....2....0....0....2....0....0....3....2....2 %e A221457 ..1....2....3....2....0....4....3....1....1....1....3....1....1....4....4....1 %Y A221457 Cf. A221459. %K A221457 nonn %O A221457 1,3 %A A221457 _R. H. Hardin_, Jan 17 2013