A304067 Number of trees with n vertices rooted at a non-edge.

0, 0, 1, 3, 9, 27, 79, 233, 679, 1987, 5784, 16864, 49063, 142821, 415439, 1208761, 3516475, 10232428, 29778138, 86682119, 252382445, 735040515, 2141319946, 6239913801, 18188637903, 53033228465, 154674931182, 451247206423

Offset

1,4

Links

Table of n, a(n) for n=1..28.

Formula

a(n) + A027852(n) = A303833(n).

Example

a(3)=1: the non-edge joins two leaves. a(4)=3: The non-edge joins two leaves of the star graph; or the non-edge joins the two leaves of the linear graph; or the non-edge joins a leaf with the node at distance 2.

Crossrefs

Cf. A000055 (not rooted), A027852 (rooted at an edge), A304068 (rooted at an oriented non-edge).

Sequence in context: A077844 A077827 A299108 * A287898 A129770 A134396

Adjacent sequences: A304064 A304065 A304066 * A304068 A304069 A304070

Keyword

nonn

Author

Brendan McKay, May 05 2018

Status

approved