A036718 -id:A036718 - cp's OEIS frontend

A244400 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 4.

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

Joerg Arndt and Alois P. Heinz, Jun 27 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Column k=4 of A244372.

Cf. A000598, A036718.

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);

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 *)

a(n) = A036718(n) - A000598(n).

A244401 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 5.

Original entry on oeis.org

1, 2, 6, 17, 50, 142, 409, 1169, 3356, 9617, 27601, 79210, 227527, 653793, 1879867, 5407806, 15564968, 44820889, 129127761, 372177974, 1073169150, 3095721985, 8933568154, 25789862435, 74477871565, 215155604291, 621754458752, 1797297119000, 5196966140656

Offset: 6

Joerg Arndt and Alois P. Heinz, Jun 27 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Column k=5 of A244372.

Cf. A036718, A036721.

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, 5$2) -`if`(k=0, 0, b(n-1$2, 4$2)):
seq(a(n), n=6..40);

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, 5, 5] - If[n == 0, 0, b[n-1, n-1, 4, 4]]; Table[a[n], {n, 6, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

a(n) = A036721(n) - A036718(n).

cp's OEIS Frontend

A244400 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 4.

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