A316796 Number of unlabeled rooted trees with n nodes where the multiplicities in the multiset of branches under any given node are distinct.
1, 1, 2, 3, 6, 11, 21, 40, 75, 139, 263, 498, 932, 1761, 3322, 6244, 11775, 22204, 41810, 78795, 148458, 279690, 527006, 993033, 1870881, 3525109, 6641904, 12514243, 23578708, 44426222, 83705148, 157713617, 297156310, 559886943, 1054911312, 1987613556
Offset: 1
Keywords
Examples
The a(6) = 11 trees: (((((o))))) ((((oo)))) (((ooo))) (((o)(o))) ((oo(o))) ((oooo)) (oo((o))) (oo(oo)) (o(o)(o)) (ooo(o)) (ooooo)
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..100
Programs
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Mathematica
strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],UnsameQ@@Length/@Split[#]&]]; Table[Length[strut[n]],{n,10}] -
PARI
C(v,n)={my(recurse(r,b,p,k)=if(!r, 1, sum(m=1, r, if(!bittest(b,m), sum(i=1, min(r\m, p), my(f=if(i==p, k+1, 1)); if(v[i]>=f, (v[i]-f+1)*self()(r-m*i, bitor(b, 1<
Extensions
Terms a(26) and beyond from Andrew Howroyd, Feb 08 2020