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A244399
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 3.
3
1, 2, 6, 16, 43, 113, 300, 787, 2074, 5460, 14391, 37960, 100275, 265187, 702307, 1862463, 4945952, 13152441, 35023003, 93385548, 249330208, 666539949, 1784102735, 4781254117, 12828545419, 34459732110, 92668129050, 249469906115, 672296028786, 1813606782459
OFFSET
4,2
LINKS
FORMULA
a(n) = A000598(n) - A001190(n+1) = A000598(n) - A036656(n+1).
a(n) ~ c * d^n / n^(3/2), where d = 1/A261340 = 2.81546003317615... and c = 0.5178759064... . - Vaclav Kotesovec, Jun 27 2014
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 3$2) -`if`(k=0, 0, b(n-1$2, 2$2)):
seq(a(n), n=4..35);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1, k, k]+j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]]//FullSimplify]; a[n_] := b[n-1, n-1, 3, 3] - If[n == 0, 0, b[n-1, n-1, 2, 2]]; Table[a[n], {n, 4, 35}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
Column k=3 of A244372.
Sequence in context: A191694 A224232 A217661 * A291142 A027994 A319503
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved