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 A109094 #14 Feb 16 2025 08:32:58 %S A109094 0,1,2,5,9,13,20,25,35,41,54,61,77,85,104,113,135,145,170,181,209,221, %T A109094 252,265,299,313,350,365,405,421,464,481,527,545,594,613,665,685,740, %U A109094 761,819,841,902,925,989,1013,1080,1105,1175,1201,1274,1301,1377,1405 %N A109094 Length of the longest path (repeated edges not allowed) between two arbitrary, distinct nodes in K_n, the complete graph on n vertices. %H A109094 R. J. Mathar, <a href="/A109094/a109094.txt">Comments on this sequence</a> %H A109094 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteGraph.html">Complete Graph.</a> %H A109094 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerPath.html">Euler Path.</a> %H A109094 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1). %F A109094 a(1)=0; a(2n+1) = n*(n-1)/2-1 = A014107(n+1), n>0; a(2n)=n*(n-2)/2+1= A001844(n-1). - _Martin Fuller_, _R. J. Mathar_ and _Mitch Harris_, Dec 06 2007 %F A109094 O.g.f.: x^2*(x^4-2*x^3-x^2-x-1)/((-1+x)^3 *(x+1)^2) . - _R. J. Mathar_, Jan 17 2008 %e A109094 a(4) = 5 because the length of the longest path between any two distinct vertices in K_4 is 5. %Y A109094 Cf. A057979, A128223. %K A109094 nonn,easy %O A109094 1,3 %A A109094 _Ryan Propper_, Jun 18 2005