cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A347479 #16 May 30 2025 01:10:42
%S A347479 11,95,31895,1652360246599,477027567058293146538340721994446103
%N A347479 Number of total dominating sets in the n-Apollonian network.
%C A347479 Term a(6) has 107 decimal digits and a(7) has 320 decimal digits. - _Andrew Howroyd_, May 29 2025
%H A347479 Andrew Howroyd, <a href="/A347479/b347479.txt">Table of n, a(n) for n = 1..8</a>
%H A347479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>.
%H A347479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>.
%o A347479 (PARI)
%o A347479 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]}
%o A347479 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
%Y A347479 Cf. A302487, A347500.
%K A347479 nonn
%O A347479 1,1
%A A347479 _Eric W. Weisstein_, Sep 03 2021
%E A347479 a(4) onwards from _Andrew Howroyd_, May 29 2025