A298422 Number of rooted trees with n nodes in which all positive outdegrees are the same.

1, 1, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 20, 2, 26, 12, 53, 2, 120, 2, 223, 43, 454, 2, 1100, 11, 2182, 215, 4902, 2, 11446, 2, 24744, 1242, 56014, 58, 131258, 2, 293550, 7643, 676928, 2, 1582686, 2, 3627780, 49155, 8436382, 2, 19809464, 50, 46027323, 321202

Offset

1,3

Comments

Row sums of A298426.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

a(n) = 2 <=> n in {A008864}. - Alois P. Heinz, Jan 20 2018

Example

The a(9) = 6 trees: ((((((((o)))))))), (o(o(o(oo)))), (o((oo)(oo))), ((oo)(o(oo))), (ooo(oooo)), (oooooooo).

Mathematica

srut[n_]:=srut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[srut/@c]]]/@Select[IntegerPartitions[n-1], Function[ptn, And@@(Divisible[#-1, Length[ptn]]&/@ptn)]], SameQ@@Length/@Cases[#, {__}, {0, Infinity}]&]];
Table[srut[n]//Length, {n, 20}]

Crossrefs

Cf. A000005, A000081, A000598, A001190, A001678, A003238, A004111, A008864, A032305, A067538, A111299, A124343, A143773, A289078, A289079, A295461, A298118, A298204, A298423, A298424, A298426.

Sequence in context: A115119 A066656 A164896 * A304716 A237984 A118136

Adjacent sequences: A298419 A298420 A298421 * A298423 A298424 A298425

Keyword

nonn

Author

Gus Wiseman, Jan 19 2018

Extensions

a(44)-a(52) from Alois P. Heinz, Jan 20 2018

Status

approved