A298123 Number of connected induced subgraphs in the n-Apollonian network.

15, 111, 38801, 2445586864035, 1080118354441207408343642986146950633

Offset: 1

Author

Eric W. Weisstein, Jan 13 2018

Keywords

• nonn

Comments

Term a(6) has 108 decimal digits and a(7) has 323 decimal digits. - Andrew Howroyd, Jan 16 2018

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..7
• Eric Weisstein's World of Mathematics, Apollonian Network
• Eric Weisstein's World of Mathematics, Connected Graph
• Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Crossrefs

Cf. A298105.

Programs

Mathematica

{1, 3, 3, 1} . # & /@ NestList[Function[{t0, t1, t2, t3}, {3 t0 + t1^3, t1^2 + t1 t2^2, t1^2 t2 + t2^2 t3, t2^3 + t3^3}] @@ # &, {1, 2, 2, 2}, 4] (* Eric W. Weisstein, Jan 17 2018 *)

PARI

\\ here t0..t3 are for 0..3 outside vertices included in set.
D(t0,t1,t2,t3)={[3*t0 + t1^3, t1^2 + t1*t2^2, t1^2*t2 + t2^2*t3, t2^3 + t3^3]}
a(n)={my(v=[1,2,2,2]); for(i=2, n, v=D(v[1], v[2], v[3], v[4])); v[1]+3*v[2]+3*v[3]+v[4]} \\ Andrew Howroyd, Jan 16 2018

Extensions

Terms a(4) and beyond from Andrew Howroyd, Jan 16 2018