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A316522 Number of unlabeled rooted trees with n nodes where all terminal rooted subtrees are either constant or strict. 0
1, 1, 2, 4, 8, 15, 34, 71, 165, 381, 913, 2193, 5389, 13287, 33155, 83196, 210251, 533956, 1363146, 3494266, 8993164, 23225281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..22.

EXAMPLE

The a(6) = 15 rooted trees:

  (((((o)))))

  ((((oo))))

  (((o(o))))

  (((ooo)))

  ((o((o))))

  ((o(oo)))

  (((o)(o)))

  ((oooo))

  (o(((o))))

  (o((oo)))

  (o(o(o)))

  (o(ooo))

  ((o)((o)))

  ((o)(oo))

  (ooooo)

Missing from this list are:

  ((oo(o)))

  (oo((o)))

  (oo(oo))

  (o(o)(o))

  (ooo(o))

MATHEMATICA

Clear[strut];

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

Table[Length[strut[n]], {n, 15}]

CROSSREFS

Cf. A000081, A003238, A004111, A214577, A276625, A316521.

Sequence in context: A061030 A036661 A145671 * A317712 A108693 A026096

Adjacent sequences:  A316519 A316520 A316521 * A316523 A316524 A316525

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 05 2018

EXTENSIONS

a(16)-a(22) from Robert Price, Sep 16 2018

STATUS

approved

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Last modified August 4 08:30 EDT 2021. Contains 346445 sequences. (Running on oeis4.)