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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, v, v, v)); v+3*v+3*v+v} \\ 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.)