

A298105


Number of connected dominating sets in the nApollonian network.


3




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



