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A316500 Number of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection. 6
1, 1, 1, 2, 3, 6, 11, 22, 46, 96, 205, 442, 976, 2146, 4789, 10719, 24202, 54841, 124967, 285724, 656011, 1510929, 3491151, 8088692, 18790084 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

The a(7) = 11 rooted identity trees:

((((((o))))))

((((o(o)))))

(((o((o)))))

((o(((o)))))

((o(o(o))))

(((o)((o))))

(o((((o)))))

(o((o(o))))

(o(o((o))))

((o)(((o))))

(o(o)((o)))

MATHEMATICA

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

Table[Length[strut[n]], {n, 20}]

CROSSREFS

Cf. A000081, A004111, A007562, A078374, A289509, A316469, A316471, A316474, A316501, A316503.

Sequence in context: A096202 A036653 A318031 * A123769 A093304 A036590

Adjacent sequences: A316497 A316498 A316499 * A316501 A316502 A316503

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 05 2018

STATUS

approved

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Last modified January 30 22:45 EST 2023. Contains 359947 sequences. (Running on oeis4.)