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 A137889 #26 Feb 16 2025 08:33:07
%S A137889 6,36,384,5460,84816,1347396,21521184,344194740,5506552176,
%T A137889 88102619556,1409633169984,22554096102420,360865400232336,
%U A137889 5773845857280516,92381531540306784,1478104495968880500,23649671900884069296,378394750275931314276,6054316003862820691584
%N A137889 Number of directed Hamiltonian paths in the n-Hanoi graph.
%H A137889 Andrew Howroyd, <a href="/A137889/b137889.txt">Table of n, a(n) for n = 1..100</a>
%H A137889 Andrew Howroyd, <a href="/A137889/a137889.txt">Hamiltonian paths in Hanoi graphs</a>
%H A137889 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H A137889 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a>
%H A137889 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24,-147,316,-192).
%F A137889 a(n) = (208 + 16*3^(n + 2) + 13*4^(n + 2) + 25*16^n)/312. - _Eric W. Weisstein_, Jun 19 2017
%F A137889 a(n) = 3*a(n-1) + (25*16^n + 64*4^n - 512)/384 for n > 1. - _Andrew Howroyd_, Jun 18 2017
%F A137889 From _Colin Barker_, Jul 30 2017: (Start)
%F A137889 G.f.: 6*x*(1 - 18*x + 67*x^2 - 60*x^3) / ((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 16*x)).
%F A137889 a(n) = 24*a(n-1) - 147*a(n-2) + 316*a(n-3) - 192*a(n-4) for n>4.
%F A137889 (End)
%t A137889 Table[(208 + 16 3^(n + 2) + 13 4^(n + 2) + 25 16^n)/312, {n, 10}] (* _Eric W. Weisstein_, Jun 19 2017 *)
%t A137889 RecurrenceTable[{a[1] == 6, a[n] == 3 a[n - 1] + (25 16^n + 64 4^n - 512)/384}, a, {n, 10}] (* _Eric W. Weisstein_, Jun 19 2017 *)
%o A137889 (PARI) a(n)=if(n==1,6,3*a(n-1) + (25*16^n + 64*4^n - 512)/384); \\ _Andrew Howroyd_, Jun 18 2017
%o A137889 (PARI) Vec(6*x*(1 - 18*x + 67*x^2 - 60*x^3) / ((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 16*x)) + O(x^30)) \\ _Colin Barker_, Jul 30 2017
%Y A137889 Cf. A288839 (chromatic polynomials of the n-Hanoi graph).
%Y A137889 Cf. A193233 (chromatic polynomial with highest coefficients first).
%Y A137889 Cf. A288490 (independent vertex sets in the n-Hanoi graph).
%Y A137889 Cf. A286017 (matchings in the n-Hanoi graph).
%Y A137889 Cf. A193136 (spanning trees of the n-Hanoi graph).
%Y A137889 Cf. A288796 (undirected paths in the n-Hanoi graph).
%K A137889 nonn,easy
%O A137889 1,1
%A A137889 _Eric W. Weisstein_, Feb 20 2008
%E A137889 Terms a(5) and beyond from _Andrew Howroyd_, Jun 18 2017