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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2018
EXTENSIONS
Name corrected by Gus Wiseman, Aug 27 2018
STATUS
approved