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A300353 Number of strict trees of weight n with odd leaves. 7
1, 1, 0, 1, 1, 2, 2, 4, 7, 14, 24, 46, 92, 186, 368, 750, 1529, 3160, 6510, 13590, 28374, 59780, 125732, 266468, 564188, 1202842, 2560106, 5484304, 11732400, 25229068, 54187918, 116938702, 252039411, 545593378, 1179545874, 2560009400, 5550315640, 12075064432 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
This sequence is initially dominated by A300352 but eventually becomes much greater.
A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.
LINKS
FORMULA
O.g.f: (1 + x/(1-x^2) + Product_{i>0} (1 + a(i)x^i))/2.
a(n) = Sum_{i=1..A000009(n)} A294018(A300351(n,i)).
EXAMPLE
The a(8) = 7 strict trees with odd leaves: (71), (53), (((51)1)1), (((31)3)1), (((31)1)3), ((31)31), ((((31)1)1)1)1).
MATHEMATICA
d[n_]:=d[n]=If[EvenQ[n], 0, 1]+Sum[Times@@d/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&UnsameQ@@#&]}];
Table[d[n], {n, 40}]
PROG
(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n] = polcoef(x/(1-x^2) + prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)); concat([1], v)} \\ Andrew Howroyd, Aug 25 2018
CROSSREFS
Sequence in context: A067953 A109070 A169973 * A049868 A120363 A118988
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 03 2018
STATUS
approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)