A335362
Triangle T(n,d) read by rows: the number of mixed trees with n>=1 nodes and 0<=d
1, 1, 1, 1, 2, 3, 2, 5, 10, 8, 3, 12, 32, 40, 27, 6, 30, 99, 178, 187, 91, 11, 74, 298, 692, 1019, 854, 350, 23, 188, 890, 2538, 4751, 5692, 4074, 1376, 47, 478, 2627, 8886, 20260, 31188, 31856, 19602, 5743, 106, 1235, 7734, 30270, 81170, 152509, 200413, 177266, 96035, 24635
Offset: 1
Examples
The triangle starts 1; 1, 1; 1, 2, 3; 2, 5,10, 8; 3,12,32,40,27; There are T(3,1)=2 mixed trees on 3 nodes with one directed edge (the edge can point towards the middle node or away from it).
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows).
- R. J. Mathar, Mixed Trees A335362
- Index entries for sequences related to trees
Crossrefs
Programs
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PARI
\\ Here R(n) is rooted mixed trees as g.f. EulerMTS(p)={my(n=serprec(p,x)-1,vars=variables(p)); exp(sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i,vars))/i))} R(n) = {my(p=x+O(x^2)); for(n=2, n, p=x*EulerMTS(2*y*p + p)); p} T(n) = {my(p=R(n)); [Vecrev(p) | p<-Vec(p + (subst(subst(p + O(x*x^(n\2)), x, x^2), y, y^2) - (2*y+1)*p^2)/2)]} { my(A=T(10)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Mar 23 2023
Extensions
Completed row n=9. - R. J. Mathar, Jun 11 2020
Terms a(46) and beyond from Andrew Howroyd, Mar 23 2023
Comments