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 A308134 #12 Feb 16 2025 08:33:55 %S A308134 3,18,192,2730,42408,673698,10760592,172097370,2753276088,44051309778, %T A308134 704816584992,11277048051210,180432700116168,2886922928640258, %U A308134 46190765770153392,739052247984440250,11824835950442034648,189197375137965657138,3027158001931410345792 %N A308134 Number of (undirected) Hamiltonian paths in the n-Hanoi graph. %H A308134 Colin Barker, <a href="/A308134/b308134.txt">Table of n, a(n) for n = 1..800</a> %H A308134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a> %H A308134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a> %H A308134 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24,-147,316,-192). %F A308134 a(n) = A137889(n)/2. %F A308134 From _Colin Barker_, Jul 19 2019: (Start) %F A308134 G.f.: 3*x*(1 - 18*x + 67*x^2 - 60*x^3) / ((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 16*x)). %F A308134 a(n) = 24*a(n-1) - 147*a(n-2) + 316*a(n-3) - 192*a(n-4) for n>4. %F A308134 a(n) = (208 + 16*3^(2+n) + 13*4^(2+n) + 25*16^n) / 624. %F A308134 (End) %o A308134 (PARI) Vec(3*x*(1 - 18*x + 67*x^2 - 60*x^3) / ((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 16*x)) + O(x^20)) \\ _Colin Barker_, Jul 19 2019 %Y A308134 Cf. A137889. %K A308134 nonn,easy %O A308134 1,1 %A A308134 _Eric W. Weisstein_, May 14 2019