A297478 Number of maximal matchings in the n-sun graph.

11, 33, 102, 344, 1241, 4719, 18785, 77917, 335502, 1495094, 6877587, 32587137, 158736257, 793609535, 4066342542, 21325689560, 114340142239, 626087871897, 3497839239743, 19921238359695, 115568831686398, 682428323156306, 4098963089083577, 25027772430177051

Offset

3,1

Links

Andrew Howroyd, Table of n, a(n) for n = 3..500

Eric Weisstein's World of Mathematics, Matching.

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set.

Eric Weisstein's World of Mathematics, Sun Graph.

Formula

a(n) = Sum_{k=0..floor(n/2)} n * (binomial(n-2+2*k, 4*k+1) + 2*binomial(n+2*k, 4*k)/(n+2*k)) * (2*k)! / (2^k*k!). - Andrew Howroyd, Jun 14 2025

a(n) ~ 2^(-1/2) * exp(2*sqrt(n) - 2 - n/2) * n^(n/2) * (1 + 23/(6*sqrt(n))). - Vaclav Kotesovec, Feb 07 2026

Prog

(PARI) a(n)={sum(k=0, n\2, n*(binomial(n-2+2*k, 4*k+1) + 2*binomial(n+2*k, 4*k)/(n+2*k))*(2*k)!/(2^k*k!) )} \\ Andrew Howroyd, Jun 14 2025

Crossrefs

Cf. A192856.

Sequence in context: A366135 A120354 A206527 * A213973 A262913 A179204

Adjacent sequences: A297475 A297476 A297477 * A297479 A297480 A297481

Keyword

nonn

Author

Eric W. Weisstein, Dec 30 2017

Extensions

a(14)-a(18) from Pontus von Brömssen, Dec 24 2022

a(19) from Eric W. Weisstein, Jul 21 2024

a(20) from Eric W. Weisstein, Aug 17 2024

a(21) onwards from Andrew Howroyd, Jun 14 2025

Status

approved