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Number of maximum independent vertex sets in the n-Sierpinski tetrahedron graph.
1

%I #21 Jul 21 2024 10:55:19

%S 4,1,8,740096,3705309419509144532503494656

%N Number of maximum independent vertex sets in the n-Sierpinski tetrahedron graph.

%H Christian Sievers, <a href="/A360131/b360131.txt">Table of n, a(n) for n = 1..7</a>

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

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

%o (PARI) rd(p)=if(p,pollead(p)*x^poldegree(p),0);

%o a(n)={my(s=[1,x,0,0,0]);for(k=2,n,s=vector(5,i,sum(wx=0,1,sum(wy=0,1,sum(wz=0,1,sum(xy=0,1,sum(xz=0,1,sum(yz=0,1,rd(s[1+(i>1)+wx+wy+wz]*s[1+(i>2)+wx+xy+xz]*s[1+(i>3)+wy+xy+yz]*s[1+(i>4)+wz+xz+yz])/x^(wx+wy+wz+xy+xz+yz)))))))));pollead([1,4,6,4,1]*s~)} \\ _Christian Sievers_, Jul 21 2024

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Jan 26 2023

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