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A324838
Number of unlabeled rooted trees with n nodes where the branches of no branch of the root form a submultiset of the branches of the root.
13
1, 0, 1, 2, 5, 10, 28, 64, 169, 422, 1108, 2872, 7627, 20202, 54216, 145867, 395288
OFFSET
1,4
EXAMPLE
The a(1) = 1 through a(6) = 10 rooted trees:
o ((o)) ((oo)) ((ooo)) ((oooo))
(((o))) (((oo))) (((ooo)))
((o)(o)) ((o)(oo))
((o(o))) ((o(oo)))
((((o)))) ((oo(o)))
((((oo))))
(((o)(o)))
(((o(o))))
((o((o))))
(((((o)))))
MATHEMATICA
submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap];
rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
Table[Length[Select[rtall[n], And@@Table[!submultQ[b, #], {b, #}]&]], {n, 10}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved