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A300440
Number of odd strict trees of weight n (all outdegrees are odd).
5
1, 1, 1, 1, 1, 2, 2, 3, 5, 7, 11, 18, 27, 45, 75, 125, 207, 353, 591, 1013, 1731, 2984, 5122, 8905, 15369, 26839, 46732, 81850, 142932, 251693, 441062, 778730, 1370591, 2425823, 4281620, 7601359, 13447298, 23919512, 42444497, 75632126, 134454505, 240100289
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2018
STATUS
approved