The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300436 Number of odd p-trees of weight n (all proper terminal subtrees have odd weight). 10
 1, 1, 1, 2, 2, 5, 5, 12, 13, 35, 37, 98, 107, 304, 336, 927, 1037, 3010, 3367, 9585, 10924, 32126, 36438, 105589, 121045, 359691, 412789, 1211214, 1398168, 4188930, 4831708, 14315544, 16636297, 50079792, 58084208, 173370663, 202101971, 611487744, 712709423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS An odd p-tree of weight n > 0 is either a single node (if n = 1) or a finite sequence of at least 3 odd p-trees whose weights are weakly decreasing odd numbers summing to n. LINKS FORMULA O.g.f: x + Product_{n odd} 1/(1 - a(n)*x^n) - Sum_{n odd} a(n)*x^n. - Gus Wiseman, Aug 27 2018 EXAMPLE The a(7) = 5 odd p-trees: ((ooo)(ooo)o), (((ooo)oo)oo), ((ooooo)oo), ((ooo)oooo), (ooooooo). MATHEMATICA b[n_]:=b[n]=If[n>1, 0, 1]+Sum[Times@@b/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&And@@OddQ/@#&]}]; Table[b[n], {n, 40}] CROSSREFS Cf. A000009, A027193, A063834, A078408, A196545, A279374, A279785, A289501, A298118, A299202, A299203, A300300, A300301, A300355, A300439, A300440. Sequence in context: A135153 A097896 A030223 * A056504 A122205 A338762 Adjacent sequences:  A300433 A300434 A300435 * A300437 A300438 A300439 KEYWORD nonn AUTHOR Gus Wiseman, Mar 05 2018 EXTENSIONS Name corrected by Gus Wiseman, Aug 27 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 11 00:43 EDT 2021. Contains 343784 sequences. (Running on oeis4.)