A300797 Number of strict trees of weight 2n + 1 in which all outdegrees and all leaves are odd.

1, 1, 1, 1, 2, 2, 4, 6, 11, 17, 34, 59, 118, 213, 424, 799, 1606, 3072, 6216, 12172, 24650, 48710, 99333, 198237, 405526, 815267, 1673127, 3387165, 6974702, 14179418, 29285048, 59841630, 123848399, 253927322, 526936694, 1084022437, 2253778793, 4649778115

Offset

0,5

Comments

A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Example

The a(7) = 6 strict trees: 15, (11 3 1), (9 5 1), (7 5 3), ((7 3 1) 3 1), ((5 3 1) 5 1).

Mathematica

a[n_]:=a[n]=If[OddQ[n], 1, 0]+Sum[Times@@a/@ptn, {ptn, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}];
Table[a[n], {n, 1, 60, 2}]

Prog

(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, 1 + v[k]*x^(2*k-1) + O(x^(2*n))) - prod(k=1, n-1, 1 - v[k]*x^(2*k-1) + O(x^(2*n))), 2*n-1)/2); v} \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000009, A000992, A032305, A063834, A078408, A089259, A196545, A273873, A279785, A289501, A298118, A300301, A300352, A300353, A300436, A300439, A300440, A300652.

Sequence in context: A339587 A293014 A124346 * A033961 A298163 A201542

Adjacent sequences: A300794 A300795 A300796 * A300798 A300799 A300800

Keyword

nonn

Author

Gus Wiseman, Mar 13 2018

Extensions

a(30)-a(37) from Alois P. Heinz, Mar 13 2018

Status

approved