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A320169 Number of balanced enriched p-trees of weight n. 9
1, 2, 3, 6, 9, 20, 31, 70, 114, 243, 415, 961, 1603, 3564, 6559, 14913, 26630, 60037, 110160, 248859, 458445, 1001190, 1882350, 4220358, 7765303, 16822107, 32307240, 70081784, 133716083, 291788153, 561823990, 1230204229, 2396185727, 5176454708, 10220127290 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An enriched p-tree of weight n is either the number n itself or a finite sequence of enriched p-trees whose weights are weakly decreasing and sum to n.

A tree is balanced if all leaves have the same height.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..500

EXAMPLE

The a(1) = 1 through a(6) = 20 balanced enriched p-trees:

  1  2     3      4           5            6

     (11)  (21)   (22)        (32)         (33)

           (111)  (31)        (41)         (42)

                  (211)       (221)        (51)

                  (1111)      (311)        (222)

                  ((11)(11))  (2111)       (321)

                              (11111)      (411)

                              ((21)(11))   (2211)

                              ((111)(11))  (3111)

                                           (21111)

                                           (111111)

                                           ((21)(21))

                                           ((22)(11))

                                           ((31)(11))

                                           ((111)(21))

                                           ((21)(111))

                                           ((211)(11))

                                           ((111)(111))

                                           ((1111)(11))

                                           ((11)(11)(11))

MATHEMATICA

eptrs[n_]:=Prepend[Join@@Table[Tuples[eptrs/@p], {p, Rest[IntegerPartitions[n]]}], n];

Table[Length[Select[eptrs[n], SameQ@@Length/@Position[#, _Integer]&]], {n, 12}]

PROG

(PARI) seq(n)={my(p=x/(1-x) + O(x*x^n), q=0); while(p, q+=p; p = 1/prod(k=1, n, 1 - polcoef(p, k)*x^k + O(x*x^n)) - 1 - p); Vec(q)} \\ Andrew Howroyd, Oct 26 2018

CROSSREFS

Cf. A000311, A000669, A001678, A005804, A048816, A079500, A119262, A120803, A141268, A196545, A289501, A319312.

Cf. A316624, A320154, A320155, A320160, A320179.

Sequence in context: A320160 A055873 A246565 * A293606 A185376 A321484

Adjacent sequences:  A320166 A320167 A320168 * A320170 A320171 A320172

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 07 2018

EXTENSIONS

Terms a(16) and beyond from Andrew Howroyd, Oct 26 2018

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)