A316796 Number of unlabeled rooted trees with n nodes where the multiplicities in the multiset of branches under any given node are distinct.

1, 1, 2, 3, 6, 11, 21, 40, 75, 139, 263, 498, 932, 1761, 3322, 6244, 11775, 22204, 41810, 78795, 148458, 279690, 527006, 993033, 1870881, 3525109, 6641904, 12514243, 23578708, 44426222, 83705148, 157713617, 297156310, 559886943, 1054911312, 1987613556

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Example

The a(6) = 11 trees:
(((((o)))))
((((oo))))
(((ooo)))
(((o)(o)))
((oo(o)))
((oooo))
(oo((o)))
(oo(oo))
(o(o)(o))
(ooo(o))
(ooooo)

Mathematica

strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], UnsameQ@@Length/@Split[#]&]];
Table[Length[strut[n]], {n, 10}]

Prog

(PARI)
C(v, n)={my(recurse(r, b, p, k)=if(!r, 1, sum(m=1, r, if(!bittest(b, m), sum(i=1, min(r\m, p), my(f=if(i==p, k+1, 1)); if(v[i]>=f, (v[i]-f+1)*self()(r-m*i, bitor(b, 1<<m), i, f)/f)))))); recurse(n, 0, #v, 0)}
seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=C(v[1..n-1], n-1)); v} \\ Andrew Howroyd, Feb 08 2020

Crossrefs

Cf. A000081, A004111, A130091, A316793, A316794, A316795.

Sequence in context: A366107 A123915 A132832 * A079116 A109222 A191789

Adjacent sequences: A316793 A316794 A316795 * A316797 A316798 A316799

Keyword

nonn

Author

Gus Wiseman, Jul 14 2018

Extensions

Terms a(26) and beyond from Andrew Howroyd, Feb 08 2020

Status

approved