cp's OEIS Frontend

A302718 Number of cycles in the n-Apollonian network.

%I A302718 #17 Feb 16 2025 08:33:53
%S A302718 7,119,27850,2635637428,40538274896917926642,
%T A302718 18915440603912727411772352213199539580794,
%U A302718 4811072124719412065599148626063536230790419188877913496386013668865001860521888965
%N A302718 Number of cycles in the n-Apollonian network.
%C A302718 a(8) has 165 decimal digits and a(9) has 331 decimal digits. - _Andrew Howroyd_, Sep 09 2019
%H A302718 Andrew Howroyd, <a href="/A302718/b302718.txt">Table of n, a(n) for n = 1..10</a>
%H A302718 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>
%H A302718 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%o A302718 (PARI)
%o A302718 P(c,d)={[2*d^3 + 7*d^2 + (6*c + 2)*d + 2*c, 3*d^2 + 5*d + (c + 1)]}
%o A302718 R(c,d)={16*d^3 + (9*c + 51)*d^2 + (30*c + 27)*d + (3*c^2 + 9*c + 4)}
%o A302718 a(n)={my(s=1, c=0, d=0); for(i=1, n, s = 3*s + R(c,d); [c,d]=P(c,d)); s} \\ _Andrew Howroyd_, Sep 10 2019
%Y A302718 Cf. A292002, A301650, A307549.
%K A302718 nonn
%O A302718 1,1
%A A302718 _Eric W. Weisstein_, Apr 14 2018
%E A302718 a(5)-a(7) from _Andrew Howroyd_, Sep 09 2019