A347479 Number of total dominating sets in the n-Apollonian network.
11, 95, 31895, 1652360246599, 477027567058293146538340721994446103
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..8
- Eric Weisstein's World of Mathematics, Apollonian Network.
- Eric Weisstein's World of Mathematics, Total Dominating Set.
Programs
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PARI
step(S,u,x)={my([e0,e1,e2,e3]=S); [e0^3 + (e1^3-u^3)*x, e1^2*e0 + e2^2*e1*x, e2*e1^2 + e3*e2^2*x, e2^3 + e3^3*x]} a(n, x=1)={my(S=[0,1+x,1+x,1+x],u=1); for(i=2, n, S=step(S,u,x); u=0); sum(k=0, 3, binomial(3, k) * S[1+k] * x^k) - 3*u*x} \\ Andrew Howroyd, May 29 2025
Extensions
a(4) onwards from Andrew Howroyd, May 29 2025
Comments