A298118 Number of unlabeled rooted trees with n nodes in which all positive outdegrees are odd.

1, 1, 1, 2, 3, 6, 11, 21, 40, 80, 159, 322, 657, 1356, 2816, 5896, 12407, 26267, 55861, 119331, 255878, 550665, 1188786, 2574006, 5588177, 12162141, 26529873, 57993624, 127020653, 278716336, 612617523, 1348680531, 2973564157, 6565313455, 14514675376

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.30984417428419893876754252289588812511559... and c = 0.5598122522173731208680575003383895445787... - Vaclav Kotesovec, Jun 04 2019

Example

The a(6) = 6 trees: (((((o))))), (((ooo))), ((oo(o))), (oo((o))), (o(o)(o)), (ooooo).

Mathematica

orut[n_]:=orut[n]=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[orut/@c]]]/@Select[IntegerPartitions[n-1], OddQ[Length[#]]&]];
Table[Length[orut[n]], {n, 15}]

Crossrefs

Cf. A000081, A000598, A003238, A004111, A027193, A032305, A067659, A290689, A291443, A297791, A298120.

Sequence in context: A006861 A052956 A351972 * A339292 A008930 A339151

Adjacent sequences: A298115 A298116 A298117 * A298119 A298120 A298121

Keyword

nonn

Author

Gus Wiseman, Jan 12 2018

Extensions

a(24)-a(35) from Alois P. Heinz, Jan 12 2018

Status

approved