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 A255114 #8 Jan 24 2018 14:30:29 %S A255114 6561,14849,19338,23463,29147,38010,49611,63075,78552,96210,116236, %T A255114 138837,164241,192698,224481,259887,299238,342882,391194,444577, %U A255114 503463,568314,639623,717915,803748,897714,1000440,1112589,1234861,1367994 %N A255114 Number of length n+7 0..2 arrays with at most one downstep in every n consecutive neighbor pairs. %C A255114 Row 7 of A255107. %H A255114 R. H. Hardin, <a href="/A255114/b255114.txt">Table of n, a(n) for n = 1..210</a> %F A255114 Empirical: a(n) = (1/120)*n^5 + (5/12)*n^4 + (187/24)*n^3 + (7393/12)*n^2 + (20667/10)*n + 1143 for n>5. %F A255114 Empirical g.f.: x*(6561 - 24517*x + 28659*x^2 - 1050*x^3 - 20126*x^4 + 11682*x^5 - 2967*x^6 + 3385*x^7 - 168*x^8 - 2466*x^9 + 1008*x^10) / (1 - x)^6. - _Colin Barker_, Jan 24 2018 %e A255114 Some solutions for n=4: %e A255114 ..0....0....1....1....1....1....0....0....0....2....1....2....2....2....0....2 %e A255114 ..1....0....0....1....1....1....1....1....1....0....0....0....0....2....1....0 %e A255114 ..1....2....0....1....0....1....1....2....1....0....0....2....0....0....0....0 %e A255114 ..1....2....2....1....1....1....1....0....1....0....0....2....0....0....0....1 %e A255114 ..2....0....2....0....1....0....0....2....2....1....1....2....0....1....2....1 %e A255114 ..1....0....1....2....1....1....0....2....0....2....1....2....1....2....2....0 %e A255114 ..1....0....1....2....2....1....1....2....0....0....2....0....2....2....2....0 %e A255114 ..1....0....2....2....2....1....1....0....1....0....0....0....0....2....2....0 %e A255114 ..1....2....2....0....0....0....2....0....1....1....2....1....0....2....0....1 %e A255114 ..0....0....2....1....2....2....0....0....1....2....2....1....0....1....0....2 %e A255114 ..2....1....2....2....2....2....1....0....2....0....2....0....2....1....0....2 %Y A255114 Cf. A255107. %K A255114 nonn %O A255114 1,1 %A A255114 _R. H. Hardin_, Feb 14 2015