A358730 Positions of first appearances in A358729 (number of nodes minus node-height).

1, 4, 8, 16, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, 13122, 19683, 39366, 59049

Offset

1,2

Comments

First differs from A334198 in having 13122 instead of 12005.

Node-height is the number of nodes in the longest path from root to leaf.

After initial terms, this appears to become A038754.

Links

Table of n, a(n) for n=1..19.

Example

The terms together with their corresponding rooted trees begin:
      1: o
      4: (oo)
      8: (ooo)
     16: (oooo)
     27: ((o)(o)(o))
     54: (o(o)(o)(o))
     81: ((o)(o)(o)(o))
    162: (o(o)(o)(o)(o))
    243: ((o)(o)(o)(o)(o))
    486: (o(o)(o)(o)(o)(o))
    729: ((o)(o)(o)(o)(o)(o))

Mathematica

MGTree[n_]:=If[n==1, {}, MGTree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
rd=Table[Count[MGTree[n], _, {0, Infinity}]-(Depth[MGTree[n]]-1), {n, 10000}];
Table[Position[rd, k][[1, 1]], {k, Union[rd]}]

Crossrefs

Positions of first appearances in A358729.

A000081 counts rooted trees, ordered A000108.

A034781 counts rooted trees by nodes and height.

A055277 counts rooted trees by nodes and leaves.

MG differences: A358580, A358724, A358726, A358729.

MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.

MG core: A000040, A000720, A001222, A007097, A056239, A112798.

Cf. A080936, A206487, A209638, A316321, A358576, A358577, A358592, A358725, A358731.

Sequence in context: A008371 A368985 A334198 * A303544 A273029 A273080

Adjacent sequences: A358727 A358728 A358729 * A358731 A358732 A358733

Keyword

nonn,more

Author

Gus Wiseman, Dec 01 2022

Status

approved