A339071 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) graphs with n nodes and k edges (n >= 1, n-1 <= k <= n*(n-1)/2).

0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 3, 2, 1, 1, 0, 1, 3, 9, 14, 12, 8, 5, 2, 1, 1, 0, 1, 4, 20, 50, 82, 94, 81, 59, 38, 20, 10, 5, 2, 1, 1, 0, 1, 6, 40, 161, 429, 780, 1076, 1197, 1114, 885, 622, 386, 215, 112, 55, 24, 11, 5, 2, 1, 1, 0, 1, 7, 70, 433, 1729, 4796

Offset

1,11

Links

Andrew Howroyd, Table of n, a(n) for n = 1..576 (rows 1..16, extracted from Robinson's tables)

R. W. Robinson, Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges, Table IV, pages 4-9.

R. W. Robinson, Tables

R. W. Robinson, Tables [Local copy, with permission]

Example

Triangle T(n,k) begins:
======================================================
n/k | 0  1  2  3  4  5  6  7  8   9  10 11 12 13 14 15
----+-------------------------------------------------
  1 | 0;
  2 |    1;
  3 |       0, 1;
  4 |          0, 1, 1, 1;
  5 |             0, 1, 2, 3, 2,  1,  1;
  6 |                0, 1, 3, 9, 14, 12, 8, 5, 2, 1, 1;
  ...

Crossrefs

Row sums are A002218.

Column sums are A010355.

Cf. A054923, A054924, A123534, A339070 (transpose), A339072.

Sequence in context: A327758 A110540 A346399 * A358478 A083475 A211994

Adjacent sequences: A339068 A339069 A339070 * A339072 A339073 A339074

Keyword

nonn,tabf

Author

Andrew Howroyd, Nov 23 2020

Status

approved