login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324844 Number of unlabeled rooted trees with n nodes where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree. 11
1, 1, 2, 3, 7, 13, 32, 71, 170, 406, 1002, 2469, 6204, 15644, 39871, 102116, 263325, 682079, 1775600, 4640220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

The a(1) = 1 through a(6) = 13 rooted trees:

  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)

          ((o))  ((oo))   ((ooo))    ((oooo))

                 (((o)))  (o(oo))    (o(ooo))

                          (((oo)))   (((ooo)))

                          ((o)(o))   ((o)(oo))

                          (o((o)))   ((o(oo)))

                          ((((o))))  (o((oo)))

                                     (oo((o)))

                                     ((((oo))))

                                     (((o)(o)))

                                     ((o((o))))

                                     (o(((o))))

                                     (((((o)))))

MATHEMATICA

submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap];

rallt[n_]:=Select[Union[Sort/@Join@@(Tuples[rallt/@#]&/@IntegerPartitions[n-1])], And@@Table[!submultQ[b, #], {b, DeleteCases[#, {}]}]&];

Table[Length[rallt[n]], {n, 10}]

CROSSREFS

The Matula-Goebel numbers of these trees are given by A324845.

Cf. A000081, A290689, A306844, A318185.

Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324843, A324846, A324847, A324848, A324849.

Sequence in context: A193530 A003120 A032131 * A007827 A250308 A259145

Adjacent sequences:  A324841 A324842 A324843 * A324845 A324846 A324847

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 18 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 3 03:14 EDT 2020. Contains 333195 sequences. (Running on oeis4.)