A298105 Number of connected dominating sets in the n-Apollonian network.

15, 96, 30208, 1562294353920, 458842788759956138092569943104028672

Offset

1,1

Comments

Term a(6) has 107 decimal digits and a(7) has 320 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 Dominating Set

Mathematica

{1, 3, 3, 1} . # & /@ NestList[Function[{t0, t1, t2, t3}, {t1^3, 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)={[t1^3, 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]}

Crossrefs

Cf. A291773, A298123.

Sequence in context: A044647 A289705 A296538 * A283168 A232296 A278203

Adjacent sequences: A298102 A298103 A298104 * A298106 A298107 A298108

Keyword

nonn

Author

Eric W. Weisstein, Jan 12 2018

Extensions

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

Status

approved