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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 27 2018
STATUS
approved