A306189 Number of minimum dominating sets in the n-Sierpinski gasket graph.

3, 6, 2, 392, 1656976026, 122836566640423857273582993856, 50043395758253154294953783566500246788902420299683914045600060272160541415159062540151890

Offset: 1

Author

Eric W. Weisstein, Jan 28 2019

Keywords

• nonn

Links

• Christian Sievers, Table of n, a(n) for n = 1..9
• Eric Weisstein's World of Mathematics, Minimum Dominating Set.
• Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Crossrefs

Cf. A347508, A347515, A376478 (domination number).

Programs

PARI

a(n)={my(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=0,3,sum(xz=0,3,sum(yz=0,3,s[1+(i>1)+!xy+!xz][1+(j>3)+(xy%2)+(xz%2)]*s[1+(i>2)+!xy+!yz][1+(j>2)+(xy\2)+(yz%2)]*s[1+(i>3)+!xz+!yz][1+(j>1)+(xz\2)+(yz\2)]/x^(!xy+!xz+!yz)))))));pollead([1,3,3,1]*vectorv(4,i,s[i][5-i]))} \\ Christian Sievers, Jul 21 2024, improved Jul 25 2024

Extensions

a(5) and beyond from Christian Sievers, Jul 21 2024