A034853 Triangle giving number of trees with n >= 3 nodes and diameter d >= 2.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 2, 1, 1, 3, 8, 7, 3, 1, 1, 3, 14, 14, 11, 3, 1, 1, 4, 21, 32, 29, 14, 4, 1, 1, 4, 32, 58, 74, 42, 19, 4, 1, 1, 5, 45, 110, 167, 128, 66, 23, 5, 1

Offset

3,8

Links

R. J. Mathar, Table of n, a(n) for n = 3..212 (a(192) corrected by Sean A. Irvine, Apr 28 2022)

B. D. McKay, Lists of Trees sorted by diameter and Homeomorphically irreducible trees, with <= 22 nodes.

B. D. McKay, Lists of Trees sorted by diameter and Homeomorphically irreducible trees, with <= 22 nodes. [Cached copy of top page only, pdf file, no active links, with permission]

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)

Index entries for sequences related to trees

Formula

Reference gives recurrence.

Example

   1
   1    1
   1    1    1
   1    2    2    1
   1    2    5    2    1
   1    3    8    7    3    1
   1    3   14   14   11    3    1
   1    4   21   32   29   14    4    1
   1    4   32   58   74   42   19    4    1
   1    5   45  110  167  128   66   23    5    1
   1    5   65  187  367  334  219   88   29    5    1
   1    6   88  322  755  850  645  328  123   34    6    1

Crossrefs

Cf. A000055 (row sums), A283826, A000094 (diameter 4), A000147 (diameter 5), A000251 (diameter 6), A000550 (diameter 7), A000306 (diameter 8).

Sequence in context: A070166 A131373 A245185 * A242093 A350910 A322058

Adjacent sequences: A034850 A034851 A034852 * A034854 A034855 A034856

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane

Status

approved