

A298123


Number of connected induced subgraphs in the nApollonian network.


2




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, VertexInduced 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



