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A298123 Number of connected induced subgraphs in the n-Apollonian network. 2
15, 111, 38801, 2445586864035, 1080118354441207408343642986146950633 (list; graph; refs; listen; history; text; internal format)
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 * A295384 A110822 A222410

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

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Last modified February 18 00:37 EST 2020. Contains 332006 sequences. (Running on oeis4.)