A324844 - OEIS

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.

1, 1, 2, 3, 7, 13, 32, 71, 170, 406, 1002, 2469, 6204, 15644, 39871, 102116, 263325, 682079, 1775600, 4640220

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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