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%I #16 Sep 10 2019 21:23:30
%S 7,119,27850,2635637428,40538274896917926642,
%T 18915440603912727411772352213199539580794,
%U 4811072124719412065599148626063536230790419188877913496386013668865001860521888965
%N Number of cycles in the n-Apollonian network.
%C a(8) has 165 decimal digits and a(9) has 331 decimal digits. - _Andrew Howroyd_, Sep 09 2019
%H Andrew Howroyd, <a href="/A302718/b302718.txt">Table of n, a(n) for n = 1..10</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%o (PARI)
%o P(c,d)={[2*d^3 + 7*d^2 + (6*c + 2)*d + 2*c, 3*d^2 + 5*d + (c + 1)]}
%o R(c,d)={16*d^3 + (9*c + 51)*d^2 + (30*c + 27)*d + (3*c^2 + 9*c + 4)}
%o 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 Cf. A292002, A301650, A307549.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Apr 14 2018
%E a(5)-a(7) from _Andrew Howroyd_, Sep 09 2019
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