A324838 - OEIS

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.

1, 0, 1, 2, 5, 10, 28, 64, 169, 422, 1108, 2872, 7627, 20202, 54216, 145867, 395288

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OFFSET

1,4

LINKS

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}]

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 18 2019

STATUS

approved