|
|
A244712
|
|
Number of 2n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) n.
|
|
2
|
|
|
0, 1, 1, 3, 6, 15, 31, 74, 159, 365, 805, 1819, 4041, 9091, 20274, 45474, 101644, 227755, 509559, 1141446, 2555232, 5723626, 12817678, 28713594, 64319189, 144104857, 322867573, 723482538, 1621264326, 3633487621, 8143682973, 18253865341, 40918282628, 91730206467
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(n, i, h, v) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
`if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember;
`if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
end:
a:= n-> b(2*n-1$2, n$2):
seq(a(n), n=0..40);
|
|
MATHEMATICA
|
b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i<1 || v<1 || n<v, 0, If[n == v, 1, Sum[Binomial[A[i, Min[i-1, h]]+j-1, j] * b[n-i*j, i-1, h, v-j], {j, 0, Min[n/i, v]}]]]];
A[n_, k_] := A[n, k] = If[n<2, n, Sum[b[n-1, n-1, j, j], {j, 1, Min[k, n-1] }]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|