cp's OEIS Frontend

A291876 Consider the graph with one central vertex connected to three outer vertices (a star graph). Then, a(n) is the minimum number of moves required to transfer a stack of n pegs from one outer vertex to another outer vertex, moving pegs to adjacent vertices, following the rules of the Towers of Hanoi.

%I A291876 #34 Feb 16 2025 08:33:51
%S A291876 2,6,12,20,32,48,66,90,122,158,206,260,324,396,492,600,728,872,1034,
%T A291876 1226,1442,1698,1986,2310,2694,3126,3612,4124,4700,5348,6116,6980,
%U A291876 7952,8976,10128,11424,12882,14418,16146,18090,20138,22442,25034,27950,31022,34478,38366
%N A291876 Consider the graph with one central vertex connected to three outer vertices (a star graph). Then, a(n) is the minimum number of moves required to transfer a stack of n pegs from one outer vertex to another outer vertex, moving pegs to adjacent vertices, following the rules of the Towers of Hanoi.
%H A291876 Robert Israel, <a href="/A291876/b291876.txt">Table of n, a(n) for n = 1..10000</a>
%H A291876 Thierry Bousch, <a href="https://www.emis.de/journals/SLC/wpapers/s77bousch.html">La Tour de Stockmeyer</a>, Séminaire Lotharingien de Combinatoire 77 (2017), Article B77d.
%H A291876 Caroline Holz auf der Heide, <a href="https://edoc.ub.uni-muenchen.de/20276/1/Holz_auf_der_Heide_Caroline.pdf">Distances and automatic sequences in distinguished variants of Hanoi graphs</a>, Dissertation. Fakultät für Mathematik, Informatik und Statistik. Ludwig-Maximilians-Universität München, 2016. [See Chapter 3.]
%H A291876 Paul K. Stockmeyer, <a href="http://www.cs.wm.edu/~pkstoc/boca.pdf"> Variations on the Four-Post Tower of Hanoi Puzzle</a>, Congr. Numer., 102 (1994), pp. 3-12.
%H A291876 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StarGraph.html">Star Graph</a>
%H A291876 <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F A291876 Conjecturally, a(n) = 2*A259823(n).
%F A291876 This conjecture was proved by Thierry Bousch, see link. - _Paul Zimmermann_, Oct 05 2015
%p A291876 A[0]:= 0:
%p A291876 A[1]:= 2:
%p A291876 for n from 2 to 100 do A[n]:= min(seq(3*A[k]+2^(n-k+1)-2, k=0..n-1)) od:
%p A291876 seq(A[i],i=1..100); # _Robert Israel_, Oct 27 2017
%Y A291876 Cf. A259823, A291877.
%K A291876 nonn
%O A291876 1,1
%A A291876 _Eric M. Schmidt_, Sep 04 2017
%E A291876 Terms a(17) and beyond from _Robert Israel_, Oct 27 2017