A358732 -id:A358732 - cp's OEIS frontend

A358107 Number of unlabeled trees covering 2n nodes, n+1 of which are leaves.

1, 1, 2, 6, 26, 119, 626, 3495, 20688, 127339, 810418, 5293790, 35351571, 240478715, 1662071181, 11646620758, 82601643511, 592110678762, 4284830131865, 31271691087861, 229980550743717, 1703097703162249, 12691879796699486, 95129358337729084, 716801612475691847

Offset: 1

Gus Wiseman, Dec 02 2022

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..100
Gus Wiseman, The a(4) = 6 trees covering 8 nodes, 5 of which are leaves.

Central column of A055290.
The labeled version is the central column of A055314.
For n leaves we have A359398.
A000272 counts trees, bisection A163395, unlabeled A000055.
A001187 counts connected graphs, unlabeled A001349.
A006125 counts graphs, unlabeled A000088.
A006129 counts covering graphs, unlabeled A002494.
A014068 counts graphs with n vertices and n-1 edges, unordered A001433.
Cf. A185650, A358732.

Terms a(11) and beyond from Andrew Howroyd, Jan 01 2023

A359398 Number of unlabeled trees covering 2n nodes, half of which are leaves.

Original entry on oeis.org

0, 1, 2, 8, 32, 158, 833, 4755, 28389, 176542, 1131055, 7432876, 49873477, 340658595, 2362652648, 16605707901, 118082160358, 848399575321, 6152038125538, 44981009272740, 331344933928536, 2457372361637286, 18337490246234464, 137612955519565773, 1038076541372187991

Offset: 1

Gus Wiseman, Jan 01 2023

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..100
Gus Wiseman, The a(4) = 8 trees covering 8 nodes, half of which are leaves.

Left of central column of A055290.
The labeled version is the left of central column of A055314.
The rooted version is A185650.
For n+1 leaves we have A358107.
The labeled version is A358732.
A000272 counts trees, bisection A163395, unlabeled A000055.
A001187 counts connected graphs, unlabeled A001349.
A006125 counts graphs, unlabeled A000088.
A006129 counts covering graphs, unlabeled A002494.
A014068 counts graphs with n vertices and n-1 edges, unlabeled A001433.

a(n) = A055290(2*n, n). - Andrew Howroyd, Jan 01 2023

Terms a(12) and beyond from Andrew Howroyd, Jan 01 2023

cp's OEIS Frontend

A358107 Number of unlabeled trees covering 2n nodes, n+1 of which are leaves.

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