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.
%I A347500 #16 Sep 03 2025 09:14:15
%S A347500 15,109,42953,2960403451017,1380531364206778111844580887042461529
%N A347500 Number of dominating sets in the n-Apollonian network.
%C A347500 Term a(6) has 108 decimal digits and a(7) has 323 decimal digits. - _Andrew Howroyd_, May 29 2025
%H A347500 Andrew Howroyd, <a href="/A347500/b347500.txt">Table of n, a(n) for n = 1..8</a>
%H A347500 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>.
%H A347500 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>.
%t A347500 Map[
%t A347500 Sum[Binomial[3, k] #[[k + 1]] x^k, {k, 0, 3}] &,
%t A347500 NestList[Function[{e0, e1, e2, e3}, {e0^3 + e1^3 x, e1^2 e0 + e2^2 e1 x, e2 e1^2 + e3 e2^2 x, e2^3 + e3^3 x}] @@ # &, {x, 1 + x, 1 + x, 1 + x}, 4]
%t A347500 ] /. x -> 1 (* _Eric W. Weisstein_, Sep 03 2025 *)
%o A347500 (PARI) \\ here e0..e3 are for 0..3 outside vertices included in dominating set.
%o A347500 step(S,x)={my([e0,e1,e2,e3]=S); [e0^3 + e1^3*x, e1^2*e0 + e2^2*e1*x, e2*e1^2 + e3*e2^2*x, e2^3 + e3^3*x]}
%o A347500 a(n,x=1)={my(S=[x,1+x,1+x,1+x]); for(i=2, n, S=step(S,x)); sum(k=0, 3, binomial(3,k) * S[1+k] * x^k)} \\ _Andrew Howroyd_, May 29 2025
%Y A347500 Cf. A291773, A298105, A347479, A347511.
%K A347500 nonn,changed
%O A347500 1,1
%A A347500 _Eric W. Weisstein_, Sep 04 2021
%E A347500 a(4) onwards from _Andrew Howroyd_, May 29 2025