A297558 Number of maximum matchings in the n-Apollonian network.

3, 32, 738, 615514464, 5030805301520123200352256, 72175948705150863615789780847197889452411340074927861143342108815392768

Offset: 1

Author

Eric W. Weisstein, Dec 31 2017

Keywords

• nonn

Comments

From Andrew Howroyd, May 30 2025: (Start)

For n >= 3, the maximum size of a matching is given by A289521(n-1). For n < 3 the maximum size is n + 1.

Term a(7) has 208 decimal digits and a(8) has 618 decimal digits. (End)

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..8
• Eric Weisstein's World of Mathematics, Apollonian Network.
• Eric Weisstein's World of Mathematics, Matching.
• Eric Weisstein's World of Mathematics, Maximum Independent Edge Set.

Crossrefs

Cf. A289521, A292429.

Programs

PARI

\\ Needs a(n,x) defined in A292429.
vector(6,n,pollead(a(n,x))) \\ Andrew Howroyd, May 30 2025

Extensions

a(5) onwards from Andrew Howroyd, May 30 2025