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A298422 Number of rooted trees with n nodes in which all positive outdegrees are the same. 44
1, 1, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 20, 2, 26, 12, 53, 2, 120, 2, 223, 43, 454, 2, 1100, 11, 2182, 215, 4902, 2, 11446, 2, 24744, 1242, 56014, 58, 131258, 2, 293550, 7643, 676928, 2, 1582686, 2, 3627780, 49155, 8436382, 2, 19809464, 50, 46027323, 321202 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row sums of A298426.
LINKS
FORMULA
a(n) = 2 <=> n in {A008864}. - Alois P. Heinz, Jan 20 2018
EXAMPLE
The a(9) = 6 trees: ((((((((o)))))))), (o(o(o(oo)))), (o((oo)(oo))), ((oo)(o(oo))), (ooo(oooo)), (oooooooo).
MATHEMATICA
srut[n_]:=srut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[srut/@c]]]/@Select[IntegerPartitions[n-1], Function[ptn, And@@(Divisible[#-1, Length[ptn]]&/@ptn)]], SameQ@@Length/@Cases[#, {__}, {0, Infinity}]&]];
Table[srut[n]//Length, {n, 20}]
CROSSREFS
Sequence in context: A115119 A066656 A164896 * A304716 A237984 A118136
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 19 2018
EXTENSIONS
a(44)-a(52) from Alois P. Heinz, Jan 20 2018
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)