A283826 Irregular triangle read by rows: T(n,k) = number of trees on n nodes with radius k, n>=1, 1 <= k <= floor(n/2).

0, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 7, 3, 1, 11, 10, 1, 1, 17, 25, 4, 1, 25, 61, 18, 1, 1, 36, 132, 61, 5, 1, 50, 277, 194, 28, 1, 1, 70, 554, 553, 117, 6, 1, 94, 1077, 1495, 451, 40, 1, 1, 127, 2034, 3823, 1552, 197, 7, 1, 168, 3770, 9427, 5020, 879, 54, 1, 1, 222, 6853, 22466, 15289, 3485, 305, 8, 1

Offset

1,7

Comments

The radius of a tree is the maximal distance of a node from the center.

Links

Table of n, a(n) for n=1..74.

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.)

Formula

T(n,k) = A034853(n,2k-1) + A034853(n,2k). - R. J. Mathar, Apr 03 2017

Example

Triangle begins:
  0,
  1,
  1,
  1,  1,
  1,  2,
  1,  4,   1,
  1,  7,   3,
  1, 11,  10,   1,
  1, 17,  25,   4,
  1, 25,  61,  18,  1,
  1, 36, 132,  61,  5,
  1, 50, 277, 194, 28, 1,
  ...

Crossrefs

Cf. A283827.

See also A000676, A000677, A027416, A102911, A004250 (column 2?), A000055 (row sums).

Sequence in context: A191525 A066633 A238415 * A088443 A117352 A137710

Adjacent sequences: A283823 A283824 A283825 * A283827 A283828 A283829

Keyword

nonn,tabf

Author

N. J. A. Sloane, Mar 19 2017

Status

approved