A370772 Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes rooted at a hedron.

0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 6, 3, 1, 1, 0, 1, 16, 10, 3, 1, 1, 0, 1, 37, 39, 10, 3, 1, 1, 0, 1, 96, 164, 48, 10, 3, 1, 1, 0, 1, 239, 746, 253, 48, 10, 3, 1, 1, 0, 1, 622, 3474, 1584, 273, 48, 10, 3, 1, 1, 0, 1, 1607, 16658, 10500, 1913, 273, 48, 10, 3, 1, 1, 0

Offset

0,12

Comments

A hedron is a (k+1)-clique.

Links

Table of n, a(n) for n=0..77.

Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.

Example

Triangle begins:
  0;
  1,   0;
  1,   1,    0;
  1,   1,    1,    0;
  1,   3,    1,    1,   0;
  1,   6,    3,    1,   1,  0;
  1,  16,   10,    3,   1,  1,  0;
  1,  37,   39,   10,   3,  1,  1, 0;
  1,  96,  164,   48,  10,  3,  1, 1, 0;
  1, 239,  746,  253,  48, 10,  3, 1, 1, 0;
  1, 622, 3474, 1584, 273, 48, 10, 3, 1, 1, 0;
  ...

Crossrefs

Columns k=1..2 are A027852, A063688(n-2).

Cf. A370770 (unrooted), A370771, A370773.

Sequence in context: A244657 A072024 A238010 * A011354 A143119 A220419

Adjacent sequences: A370769 A370770 A370771 * A370773 A370776 A370777

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 01 2024

Status

approved