A347479 Number of total dominating sets in the n-Apollonian network.

11, 95, 31895, 1652360246599, 477027567058293146538340721994446103

Offset: 1

Author

Eric W. Weisstein, Sep 03 2021

Keywords

• nonn

Comments

Term a(6) has 107 decimal digits and a(7) has 320 decimal digits. - Andrew Howroyd, May 29 2025

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.

Crossrefs

Cf. A302487, A347500.

Programs

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