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

1,1

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.

Prog

(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

Crossrefs

Sequence in context: A088730 A058956 A010257 * A334567 A284863 A121068

Adjacent sequences: A381372 A381373 A381374 * A381376 A381377 A381378

Keyword

nonn

Author

Eric W. Weisstein, May 12 2025

Extensions

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

Status

approved