A387435 Number of dominating sets in the n-Dorogovtsev-Goltsev-Mendes graph.

3, 7, 45, 13293, 461504710485, 37306936154345310416554765472710125

Offset: 0

Author

Eric W. Weisstein, Aug 29 2025

Keywords

• nonn
• new

Comments

a(6) has 104 decimal digits. - Andrew Howroyd, Aug 31 2025

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..8
• Eric Weisstein's World of Mathematics, Dominating Set.
• Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.

Crossrefs

Cf. A115098 (domination number), A368456.

Programs

Mathematica

Join[{3}, Map[{1, 2, 1} . # &, NestList[Function[{p2, q1, q2}, {p2 (p2^2 + q1^2), q1^2 (q2 + p2), q2 (q1^2 + q2^2)}] @@ # &, {1, 2, 2}, 7]]] (* Eric W. Weisstein, Sep 03 2025 *)

PARI

step(v)={my([p2,q1,q2]=v); [p2*(p2^2+q1^2), q1^2*(q2+p2), q2*(q1^2+q2^2)]}
a(n)={if(n==0, 3, my(v=[1,2,2]); for(i=2, n, v=step(v)); v[1]+2*v[2]+v[3])} \\ Andrew Howroyd, Aug 31 2025

Extensions

a(4) onwards from Andrew Howroyd, Aug 29 2025