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

Author

Eric W. Weisstein, Dec 30 2017

Keywords

• nonn

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.

Crossrefs

Cf. A192856.

Programs

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

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

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