A334827 The number of oriented star-like and star trees with n arcs.

4, 17, 66, 221, 688, 2034, 5788, 15998, 43192, 114496, 298712, 769340, 1959064, 4940761, 12354210, 30660947, 75583868, 185208833, 451356846, 1094522547, 2642121008, 6351335083, 15208854510, 36288478177, 86295204732, 204571273167, 483532711338, 1139738858221

Offset: 3

Author

R. J. Mathar, Jun 09 2020

Keywords

• nonn

Examples

			a(6)=221 counts 132 oriented star-like trees with 3 rays and 6 arcs, 62 with 4 rays and 6 arcs, 20 with 5 rays and 6 arcs, and 7 star trees. In the illustrations in A000238 [Mathar] this is the same as 48 (shape 2) + 64 (shape 3) + 20 (shape 4) +32 (shape 7) + 30 (shape 8) +20 (shape 10) + 7 (shape 11).
		

Links

• Wikipedia, Starlike Tree
• Index entries for sequences related to trees

Crossrefs

Cf. A000238 (oriented trees), A051437 (linear oriented trees), A209406 (star-like oriented by number of arcs and rays), A004250 (undirected edges).

Formula

a(n) = A034899(n) -2^(n+1) = Sum_{k>=3} A209406(n,k).