A381375 Number of minimum dominating sets in the n-Hanoi graph.

3, 27, 9, 2166, 45, 371643, 261, 77055612, 1557, 16530541953, 9333, 3566560502166, 55989, 770233227440127, 335925, 166365249148401792, 2015541, 35934710960120160093, 12093237, 7761891045770533947786, 72559413, 1676568233248144889168571, 435356469

Offset: 1

Author

Eric W. Weisstein, May 12 2025

Keywords

• nonn

Links

• Christian Sievers, Table of n, a(n) for n = 1..857
• Eric Weisstein's World of Mathematics, Hanoi Graph.
• Eric Weisstein's World of Mathematics, Minimum Dominating Set.

Programs

PARI

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

Extensions

a(6) and beyond from Christian Sievers, May 23 2025