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 A255665 #6 May 25 2024 23:59:47 %S A255665 4096,16384,64257,209412,564600,1324872,2816673,5555336,10323148, %T A255665 18270784,31047630,50967648,81218758,126125244,191474454,284921080, %U A255665 416484596,599158024,849649115,1189278300,1645061412,2251009232 %N A255665 Number of length n+5 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs. %C A255665 Row 5 of A255660. %H A255665 R. H. Hardin, <a href="/A255665/b255665.txt">Table of n, a(n) for n = 1..210</a> %F A255665 Empirical: a(n) = (1/39916800)*n^11 + (11/3628800)*n^10 + (1/6048)*n^9 + (125/24192)*n^8 + (315821/1209600)*n^7 + (994223/172800)*n^6 + (4372667/72576)*n^5 + (6881047/36288)*n^4 + (208795429/151200)*n^3 - (13877413/12600)*n^2 - (30361/231)*n + 712 for n>3. %e A255665 Some solutions for n=3 %e A255665 ..1....0....2....2....3....2....2....0....2....2....1....1....1....1....2....2 %e A255665 ..2....1....2....0....1....2....3....0....2....2....1....0....0....2....3....1 %e A255665 ..1....1....1....1....0....0....2....3....3....0....0....1....3....2....2....1 %e A255665 ..3....2....2....1....0....3....3....0....2....3....1....1....3....3....3....3 %e A255665 ..0....0....2....1....3....1....3....3....0....2....1....2....1....0....2....3 %e A255665 ..0....0....0....0....1....1....1....1....3....0....3....0....0....2....2....2 %e A255665 ..3....3....3....2....0....0....2....1....2....1....1....3....0....2....3....2 %e A255665 ..1....3....2....1....3....1....2....1....1....3....2....0....0....2....0....1 %Y A255665 Cf. A255660. %K A255665 nonn %O A255665 1,1 %A A255665 _R. H. Hardin_, Mar 01 2015