A352460 Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.

1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 2, 1, 1, 5, 4, 3, 2, 1, 1, 9, 6, 5, 3, 2, 1, 1, 13, 10, 6, 5, 3, 2, 1, 1, 23, 15, 10, 7, 5, 3, 2, 1, 1, 35, 24, 14, 10, 7, 5, 3, 2, 1, 1, 61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1, 98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1

Offset

3,4

Links

Table of n, a(n) for n=3..80.

Example

Triangle begins:
    1;
    1,  1;
    2,  1,  1;
    2,  2,  1,  1;
    4,  3,  2,  1,  1;
    5,  4,  3,  2,  1,  1;
    9,  6,  5,  3,  2,  1, 1;
   13, 10,  6,  5,  3,  2, 1, 1;
   23, 15, 10,  7,  5,  3, 2, 1, 1;
   35, 24, 14, 10,  7,  5, 3, 2, 1, 1;
   61, 39, 23, 14, 11,  7, 5, 3, 2, 1, 1;
   98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1;
In particular, the rooted trees counted in the first three rows of the triangle are shown by using the Hasse diagram as follows:
  ---------
    o   o
     \ /
      o
  ----------------------
    o       |
    |       |
    o   o   |   o  o  o
     \ /    |    \ | /
      o     |      o
  ------------------------------------------------------
    o   o        o   o   |   o         |
     \ /         |   |   |   |         |
      o   o      o   o   |   o  o  o   |   o  o   o  o
       \ /        \ /    |    \ | /    |    \  \ /  /
        o          o     |      o      |        o

Crossrefs

Cf. A000081, A000598, A001190, A292556, A299038.

Sequence in context: A106476 A101566 A331447 * A342767 A176653 A174842

Adjacent sequences: A352457 A352458 A352459 * A352461 A352462 A352463

Keyword

nonn,tabl

Author

Salah Uddin Mohammad, Mar 17 2022

Status

approved