A381375 - OEIS

%I #29 May 23 2025 20:02:45

%S 3,27,9,2166,45,371643,261,77055612,1557,16530541953,9333,

%T 3566560502166,55989,770233227440127,335925,166365249148401792,

%U 2015541,35934710960120160093,12093237,7761891045770533947786,72559413,1676568233248144889168571,435356469

%N Number of minimum dominating sets in the n-Hanoi graph.

%H Christian Sievers, <a href="/A381375/b381375.txt">Table of n, a(n) for n = 1..857</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>.

%o (PARI)

%o lista(n)={my(l=List([3]),t=[[0,2],[1,1],[1, 2],[2,0],[2,1],[2,2]],s=[[1+O(x),0,0,0],[0,0,x+O(x^2)],[0,x^2+O(x^3)],[x^3+O(x^4)]]);for(k=2,n,s=vector(4,i,vector(5-i,j,sum(xy=1,#t,sum(xz=1,#t,sum(yz=1,#t,s[1+(i>1)+(t[xy][1]==2)+(t[xz][1]==2)][1+(j>3)+(t[xy][1]==1)+(t[xz][1]==1)]*s[1+(i>2)+(t[xy][2]==2)+(t[yz][1]==2)][1+(j>2)+(t[xy][2]==1)+(t[yz][1]==1)]*s[1+(i>3)+(t[xz][2]==2)+(t[yz][2]==2)][1+(j>1)+(t[xz][2]==1)+(t[yz][2]==1)])))));s/=x^(valuation(vecsum(vector(4,i,vecsum(s[i])))));listput(l,pollead([1,3,3,1]*vectorv(4,i,s[i][5-i]))));l} \\ _Christian Sievers_, May 23 2025

%K nonn

%O 1,1

%A _Eric W. Weisstein_, May 12 2025

%E a(6) and beyond from _Christian Sievers_, May 23 2025