A244454 -id:A244454 - cp's OEIS frontend

A244463 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 9.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 7, 12, 16, 21, 25, 30, 34, 39, 47, 61, 83, 117, 160, 215, 280, 356, 442, 549, 682, 864, 1112, 1458, 1919, 2533, 3313, 4298, 5521, 7057, 8995, 11497, 14751, 19042, 24687, 32102, 41731, 54172, 70112, 90535

Offset: 10

Joerg Arndt and Alois P. Heinz, Jun 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..900

Column k=9 of A244454.

Cf. A244538.

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, 9$2) -b(n-1$2, 10$2):
seq(a(n), n=10..75);

A244464 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 10.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 7, 12, 16, 21, 25, 30, 34, 39, 43, 52, 65, 88, 121, 165, 219, 285, 360, 447, 544, 661, 805, 998, 1256, 1613, 2085, 2709, 3500, 4496, 5709, 7201, 9016, 11277, 14108, 17738, 22410, 28484, 36330

Offset: 11

Joerg Arndt and Alois P. Heinz, Jun 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 11..900

Column k=10 of A244454.

Cf. A244539.

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, 10$2) -b(n-1$2, 11$2):
seq(a(n), n=11..80);

cp's OEIS Frontend

A244463 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 9.

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