login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316694 Number of lone-child-avoiding locally disjoint rooted identity trees whose leaves form an integer partition of n. 16
1, 1, 2, 3, 6, 13, 28, 62, 143, 338, 804, 1948, 4789, 11886, 29796, 75316, 191702, 491040, 1264926, 3274594, 8514784, 22229481, 58243870 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A rooted tree is lone-child-avoiding if every non-leaf node has at least two branches. It is locally disjoint if no branch overlaps any other (unequal) branch of the same root. It is an identity tree if no branch appears multiple times under the same root.
LINKS
EXAMPLE
The a(7) = 28 rooted trees:
7,
(16),
(25),
(1(15)),
(34),
(1(24)), (2(14)), (4(12)), (124),
(1(1(14))),
(3(13)),
(2(23)),
(1(1(23))), (1(2(13))), (1(3(12))), (1(123)), (2(1(13))), (3(1(12))), (12(13)), (13(12)),
(1(1(1(13)))),
(2(2(12))),
(1(1(2(12)))), (1(2(1(12)))), (1(12(12))), (2(1(1(12)))), (12(1(12))),
(1(1(1(1(12))))).
Missing from this list but counted by A300660 are ((12)(13)) and ((12)(1(12))).
MATHEMATICA
disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], And[UnsameQ@@#, disjointQ[#]]&], {ptn, Rest[IntegerPartitions[n]]}], {n}];
Table[Length[nms[n]], {n, 10}]
CROSSREFS
The semi-identity tree version is A212804.
Not requiring local disjointness gives A300660.
The non-identity tree version is A316696.
This is the case of A331686 where all leaves are singletons.
Rooted identity trees are A004111.
Locally disjoint rooted identity trees are A316471.
Lone-child-avoiding locally disjoint rooted trees are A331680.
Locally disjoint enriched identity p-trees are A331684.
Sequence in context: A032143 A032160 A089735 * A000646 A316770 A197463
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 10 2018
EXTENSIONS
a(21)-a(23) from Robert Price, Sep 16 2018
Updated with corrected terminology by Gus Wiseman, Feb 06 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)