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

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy
• nice

Examples

			   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
		

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

Crossrefs

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

Formula

Reference gives recurrence.