A292708 - OEIS

%I #10 Jul 20 2024 08:10:47

%S 4,14,440,14115134,466518785395590988060,

%T 16843102905928252175005299732280541221280287736370800875201510

%N Number of independent vertex sets and vertex covers in the n-Sierpinski sieve graph.

%H Christian Sievers, <a href="/A292708/b292708.txt">Table of n, a(n) for n = 1..8</a>

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

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

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

%o (PARI) a(n)={my(s=[1,1,0,0]);for(k=2,n,s=vector(4,i,sum(xy=0,1,sum(xz=0,1,sum(yz=0,1, s[1+(i>1)+xy+xz]*s[1+(i>2)+xy+yz]*s[1+(i>3)+xz+yz])))));[1,3,3,1]*s~} \\ _Christian Sievers_, Jul 20 2024

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Sep 21 2017

%E a(6) and beyond from _Christian Sievers_, Jul 20 2024