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A244704 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 3. 2
1, 1, 3, 6, 13, 25, 55, 107, 224, 454, 938, 1916, 3969, 8163, 16918, 35010, 72724, 151093, 314749, 656115, 1370348, 2864948, 5998547, 12572884, 26385837, 55431031, 116577538, 245415158, 517152607, 1090771973, 2302729115, 4865449045, 10288826434, 21774842539 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,3
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
a(n) ~ c * d^n / n^(3/2), where d = 2.1991393868..., c = 1.0259536... . - Vaclav Kotesovec, Aug 27 2014
EXAMPLE
a(7) = 6:
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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(n-1$2, 3$2):
seq(a(n), n=4..50);
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]}]];
a[n_] := b[n-1, n-1, 3, 3];
a /@ Range[4, 50] (* Jean-François Alcover, Dec 27 2020, after Alois P. Heinz *)
CROSSREFS
Column k=3 of A244657.
Sequence in context: A121349 A215984 A074890 * A032198 A079941 A255125
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 04 2014
STATUS
approved

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Last modified March 28 15:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)