login
A244400
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 4.
2
1, 2, 6, 17, 49, 136, 386, 1081, 3044, 8549, 24052, 67642, 190426, 536205, 1510920, 4259418, 12014682, 33907056, 95740913, 270468869, 764450150, 2161638413, 6115252839, 17307553766, 49005101669, 138811296158, 393351362321, 1115072623713, 3162183392471
OFFSET
5,2
LINKS
FORMULA
a(n) = A036718(n) - A000598(n).
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, 4$2) -`if`(k=0, 0, b(n-1$2, 3$2)):
seq(a(n), n=5..40);
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, 4, 4] - If[n == 0, 0, b[n-1, n-1, 3, 3]]; Table[a[n], {n, 5, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
Column k=4 of A244372.
Sequence in context: A365244 A036365 A299162 * A052536 A122100 A122099
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved