A302718 Number of cycles in the n-Apollonian network.

7, 119, 27850, 2635637428, 40538274896917926642, 18915440603912727411772352213199539580794, 4811072124719412065599148626063536230790419188877913496386013668865001860521888965

Offset: 1

Author

Eric W. Weisstein, Apr 14 2018

Keywords

• nonn

Comments

a(8) has 165 decimal digits and a(9) has 331 decimal digits. - Andrew Howroyd, Sep 09 2019

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10
• Eric Weisstein's World of Mathematics, Apollonian Network
• Eric Weisstein's World of Mathematics, Graph Cycle

Crossrefs

Cf. A292002, A301650, A307549.

Programs

PARI

P(c,d)={[2*d^3 + 7*d^2 + (6*c + 2)*d + 2*c, 3*d^2 + 5*d + (c + 1)]}
R(c,d)={16*d^3 + (9*c + 51)*d^2 + (30*c + 27)*d + (3*c^2 + 9*c + 4)}
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

Extensions

a(5)-a(7) from Andrew Howroyd, Sep 09 2019