OFFSET
1,6
COMMENTS
An odd strict tree of weight n is either a single node of weight n, or a finite odd-length sequence of at least 3 odd strict trees with strictly decreasing weights summing to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
EXAMPLE
The a(10) = 7 odd strict trees: 10, (721), (631), (541), (532), ((421)21), ((321)31).
MATHEMATICA
g[n_]:=g[n]=1+Sum[Times@@g/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}];
Array[g, 20]
PROG
(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)) - prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)), n)/2); v} \\ Andrew Howroyd, Aug 25 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2018
STATUS
approved