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 A292429 #59 May 30 2025 15:47:51
%S A292429 10,99,38613,377686178656,28685416388231593782505635840000
%N A292429 Number of matchings in the n-Apollonian network.
%C A292429 Term a(6) has 90 decimal digits and a(7) has 264 decimal digits. - _Andrew Howroyd_, May 30 2025
%H A292429 Andrew Howroyd, <a href="/A292429/b292429.txt">Table of n, a(n) for n = 1..8</a>
%H A292429 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>.
%H A292429 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>.
%H A292429 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>.
%o A292429 (PARI) \\ here m0..m3 are 0..3 outside vertices matched internally.
%o A292429 step(S,x)={my([m0,m1,m2,m3]=S); [ m0^3 + 3*m0^2*m1, 2*m0^2*m1 + 4*m0*m1^2 + 2*m0^2*m2 + m0^3*x, m0^2*m2 + 3*m0*m1^2 + 8*m0*m1*m2 + m0^2*m3 + 3*m1^3 + 4*m0^2*m1*x, 6*m0*m1*m2 + 2*m1^3 + 12*m1^2*m2 + 6*m0*m2^2 + 6*m0*m1*m3 + 3*(m0^2*m2 + 3*m0*m1^2)*x ]}
%o A292429 a(n, x=1)={my(S=[1,0,0,0]); for(i=1, n, S=step(S,x)); sum(k=0, 3, binomial(3, k) * S[1+k]) + 3*(S[1]+S[2])*x} \\ _Andrew Howroyd_, May 30 2025
%Y A292429 Cf. A297558.
%K A292429 nonn
%O A292429 1,1
%A A292429 _Eric W. Weisstein_, Sep 30 2017
%E A292429 a(5) onwards from _Andrew Howroyd_, May 30 2025