A283826 -id:A283826 - cp's OEIS frontend

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

N. J. A. Sloane

			   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

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

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

Reference gives recurrence.

A324239 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with radius k, (0 <= k <= floor(n/2)).

Original entry on oeis.org

1, 0, 1, 0, 2, 0, 4, 2, 0, 11, 10, 0, 34, 76, 2, 0, 156, 682, 15, 0, 1044, 9864, 207, 2, 0, 12346, 245518, 3197, 19, 0, 274668, 11366961, 74614, 326, 2

Offset: 1

Andrew Howroyd, Sep 02 2019

			Triangle begins:
  1;
  0,      1;
  0,      2;
  0,      4,        2;
  0,     11,       10;
  0,     34,       76,     2;
  0,    156,      682,    15;
  0,   1044,     9864,   207,   2;
  0,  12346,   245518,  3197,  19;
  0, 274668, 11366961, 74614, 326, 2;
  ...

Eric Weisstein's World of Mathematics, Graph Radius
Wikipedia, Distance (graph theory)

Row sums give A001349.
Columns k=1..2 are A000088(n-1), A324061.
Cf. A283826, A294522, A294525, A324244.

A283827 Irregular triangle read by rows: T(n,k) = number of trees on n nodes with load k, n>=1, 1 <= k <= floor(n/2).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 3, 7, 1, 3, 9, 10, 1, 4, 12, 30, 1, 4, 18, 38, 45, 1, 5, 21, 64, 144, 1, 5, 27, 91, 217, 210

Offset: 1

N. J. A. Sloane, Mar 19 2017

The load of a tree is the maximal branch weight from the centroid.

			Triangle begins:
  0,
  1,
  1,
  1, 1,
  1, 2,
  1, 2,  3,
  1, 3,  7,
  1, 3,  9, 10,
  1, 4, 12, 30,
  1, 4, 18, 38,  45,
  1, 5, 21, 64, 144,
  1, 5, 27, 91, 217, 210,
  ...

Peter Steinbach, Field Guide to Simple Graphs, Volume 3, Part 8 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Cf. A283826.

See also A000676, A000677, A027416, A102911.

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A324239 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with radius k, (0 <= k <= floor(n/2)).

Views

Author

Keywords

Examples

Links

Crossrefs

A283827 Irregular triangle read by rows: T(n,k) = number of trees on n nodes with load k, n>=1, 1 <= k <= floor(n/2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs