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A244457 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 3. 3
1, 0, 0, 1, 2, 2, 4, 7, 12, 20, 34, 56, 98, 167, 284, 484, 835, 1433, 2467, 4250, 7345, 12700, 22004, 38154, 66266, 115224, 200623, 349654, 610126, 1065739, 1863547, 3261672, 5714277, 10020092, 17586014, 30890654, 54305289, 95542387, 168221056, 296401979 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,5
LINKS
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 1.8239199077079..., c = 0.49573400799... . - Vaclav Kotesovec, Jul 11 2014
EXAMPLE
a(7) = 1:
o
/|\
o o o
/|\
o o o
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, max(0, t-j), k), j=0..n/i)))
end:
a:= n-> b(n-1$2, 3$2) -b(n-1$2, 4$2):
seq(a(n), n=4..45);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 3, 3] - b[n - 1, n - 1, 4, 4]; Table[a[n], {n, 4, 45}] (* Jean-François Alcover, Feb 06 2015, after Maple *)
CROSSREFS
Column k=3 of A244454.
Cf. A244532.
Sequence in context: A095325 A179183 A325786 * A325908 A153970 A067953
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 29 2014
STATUS
approved

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Last modified June 18 01:17 EDT 2024. Contains 373468 sequences. (Running on oeis4.)