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A318485 Number of p-trees of weight 2n + 1 in which all outdegrees are odd. 1
1, 1, 2, 5, 13, 37, 107, 336, 1037, 3367, 10924, 36438, 121045, 412789, 1398168, 4831708, 16636297, 58084208, 202101971, 712709423, 2502000811, 8880033929, 31428410158, 112199775788, 399383181020, 1433385148187, 5128572792587, 18481258241133 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A p-tree of weight n with odd outdegrees is either a single node (if n = 1) or a finite odd-length sequence of at least 3 p-trees with odd outdegrees whose weights are weakly decreasing and sum to n.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

EXAMPLE

The a(4) = 13 p-trees of weight 9 with odd outdegrees:

  ((((ooo)oo)oo)oo)

  (((ooo)(ooo)o)oo)

  (((ooo)oo)(ooo)o)

  ((ooo)(ooo)(ooo))

  (((ooooo)oo)oo)

  (((ooo)oooo)oo)

  ((ooooo)(ooo)o)

  (((ooo)oo)oooo)

  ((ooo)(ooo)ooo)

  ((ooooooo)oo)

  ((ooooo)oooo)

  ((ooo)oooooo)

  (ooooooooo)

MATHEMATICA

b[n_]:=b[n]=If[n>1, 0, 1]+Sum[Times@@b/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&]}];

Table[b[n], {n, 1, 20, 2}]

PROG

(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n] = polcoef(1/prod(k=1, n-1, 1 - v[k]*x^(2*k-1) + O(x^(2*n))) - 1/prod(k=1, n-1, 1 + v[k]*x^(2*k-1) + O(x^(2*n))), 2*n-1)/2); v} \\ Andrew Howroyd, Aug 27 2018

CROSSREFS

Cf. A027193, A063834, A078408, A196545, A279374, A289501, A298118, A300300, A300301, A300355, A300436, A300647, A300652, A300797, A302243.

Sequence in context: A233281 A218551 A293297 * A005961 A036249 A126031

Adjacent sequences:  A318482 A318483 A318484 * A318486 A318487 A318488

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 27 2018

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)