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A304067
Number of trees with n vertices rooted at a non-edge.
2
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
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
KEYWORD
nonn
AUTHOR
Brendan McKay, May 05 2018
STATUS
approved