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

15, 111, 38801, 2445586864035, 1080118354441207408343642986146950633

Offset

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A298105.

Sequence in context: A222117 A105051 A105040 * A370763 A295384 A110822

Adjacent sequences: A298120 A298121 A298122 * A298124 A298125 A298126

Keyword

nonn

Author

Eric W. Weisstein, Jan 13 2018

Extensions

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

Status

approved