|
%I #14 Jan 17 2018 07:49:25
%S 15,111,38801,2445586864035,1080118354441207408343642986146950633
%N Number of connected induced subgraphs in the n-Apollonian network.
%C Term a(6) has 108 decimal digits and a(7) has 323 decimal digits. - _Andrew Howroyd_, Jan 16 2018
%H Andrew Howroyd, <a href="/A298123/b298123.txt">Table of n, a(n) for n = 1..7</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%t {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 *)
%o (PARI) \\ here t0..t3 are for 0..3 outside vertices included in set.
%o D(t0,t1,t2,t3)={[3*t0 + t1^3, t1^2 + t1*t2^2, t1^2*t2 + t2^2*t3, t2^3 + t3^3]}
%o 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
%Y Cf. A298105.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jan 13 2018
%E Terms a(4) and beyond from _Andrew Howroyd_, Jan 16 2018
|
