A306189 - OEIS

%I #16 Feb 16 2025 08:33:54

%S 3,6,2,392,1656976026,122836566640423857273582993856,

%T 50043395758253154294953783566500246788902420299683914045600060272160541415159062540151890

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

%H Christian Sievers, <a href="/A306189/b306189.txt">Table of n, a(n) for n = 1..9</a>

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

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

%o (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

%K nonn,changed

%O 1,1

%A _Eric W. Weisstein_, Jan 28 2019

%E a(5) and beyond from _Christian Sievers_, Jul 21 2024