A306201 Number of unlabeled balanced rooted semi-identity trees with n nodes.

0, 1, 1, 2, 3, 4, 6, 8, 12, 16, 25, 35, 53, 77, 117, 173, 265, 396, 605, 919, 1408, 2147, 3305, 5070, 7819, 12049, 18635, 28811, 44672, 69264, 107618, 167292, 260446, 405686, 632743, 987441, 1542555, 2411208, 3772247, 5905002, 9250436, 14499234, 22740910, 35686092

Offset

0,4

Comments

A rooted tree is a semi-identity tree if the non-leaf branches of the root are all distinct and are themselves semi-identity trees. It is balanced if all leaves are the same distance from the root. The only balanced identity trees are rooted paths.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Example

The a(1) = 1 through a(7) = 8 balanced rooted semi-identity trees:
  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)      (oooooo)
          ((o))  ((oo))   ((ooo))    ((oooo))     ((ooooo))
                 (((o)))  (((oo)))   (((ooo)))    (((oooo)))
                          ((((o))))  ((o)(oo))    ((o)(ooo))
                                     ((((oo))))   ((((ooo))))
                                     (((((o)))))  (((o)(oo)))
                                                  (((((oo)))))
                                                  ((((((o))))))

Mathematica

ursit[n_]:=Join@@Table[Select[Union[Sort/@Tuples[ursit/@ptn]], UnsameQ@@DeleteCases[#, {}]&], {ptn, IntegerPartitions[n-1]}];
Table[Length[Select[ursit[n], SameQ@@Length/@Position[#, {}]&]], {n, 10}]

Crossrefs

Cf. A000081, A004111, A048816, A079500, A120803, A306200, A316624, A317712, A320169, A320270.

Row sums of A306269.

Sequence in context: A068927 A336613 A018261 * A218935 A018438 A342338

Adjacent sequences: A306198 A306199 A306200 * A306202 A306203 A306204

Keyword

nonn

Author

Gus Wiseman, Jan 29 2019

Extensions

More terms from Alois P. Heinz, Jan 29 2019

Status

approved