A347508 - OEIS

%I #14 Jul 21 2024 12:48:35

%S 7,45,19779,1594379844635,835901871677190536135654070191409955

%N Number of dominating sets in the n-Sierpinski sieve graph.

%C a(6) has 108 decimal digits.

%H Christian Sievers, <a href="/A347508/b347508.txt">Table of n, a(n) for n = 1..8</a> (1..6 from Andrew Howroyd)

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiSieveGraph.html">Sierpinski Sieve Graph</a>

%o (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

%Y Cf. A306189, A347484, A347515.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Sep 04 2021

%E Terms a(4) and beyond from _Andrew Howroyd_, Jan 19 2022