A347508 Number of dominating sets in the n-Sierpinski gasket graph.

7, 45, 19779, 1594379844635, 835901871677190536135654070191409955

Offset: 1

Author

Eric W. Weisstein, Sep 04 2021

Keywords

• nonn

Comments

a(6) has 108 decimal digits.

Links

• Christian Sievers, Table of n, a(n) for n = 1..8 (1..6 from Andrew Howroyd)
• Eric Weisstein's World of Mathematics, Dominating Set.
• Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Crossrefs

Cf. A306189, A347484, A347515, A373442.

Programs

PARI

a(n)={my(s=[[1,0,0,0],[0,0,1],[0,1],[1]]);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)]))))));[1,3,3,1]*vectorv(4,i,s[i][5-i])} \\ Christian Sievers, Jul 21 2024

Extensions

Terms a(4) and beyond from Andrew Howroyd, Jan 19 2022