A339069 Triangle read by rows: T(n,k) is the number of unlabeled series-reduced 2-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).

1, 1, 1, 1, 2, 4, 5, 4, 2, 1, 1, 4, 17, 30, 34, 29, 17, 9, 5, 2, 1, 1, 5, 33, 133, 307, 464, 505, 438, 310, 188, 103, 52, 23, 11, 5, 2, 1, 1, 25, 277, 1352, 3953, 7939, 11897, 14131, 13827, 11465, 8235, 5226, 2966, 1537, 737, 333, 144, 62, 25, 11, 5, 2, 1, 1

Offset

4,5

Links

Andrew Howroyd, Table of n, a(n) for n = 4..732 (rows n=4..18, extracted from Robinson's tables)

R. W. Robinson, Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges, Table V, pages 10-18.

R. W. Robinson and T. R. S. Walsh, Inversion of cycle index sum relations for 2- and 3-connected graphs, J. Combin. Theory Ser. B. 57 (1993), 289-308.

Example

Triangle begins:
===========================================================
n/k | 6  7  8   9  10 11  12  13  14  15  16 17 18 19 20 21
----+------------------------------------------------------
  4 | 1;
  5 |       1,  1,  1;
  6 |           2,  4, 5,  4,  2,  1,  1;
  7 |                  4, 17, 30, 34, 29, 17, 9, 5, 2, 1, 1;
  8 |                      5, 33 ...
  ...

Crossrefs

Row sums are A006289.

Column sums are A339068.

Cf. A123545, A123546, A339071, A339072.

Sequence in context: A011174 A123545 A123546 * A334422 A317499 A004581

Adjacent sequences: A339066 A339067 A339068 * A339070 A339071 A339072

Keyword

nonn,tabf

Author

Andrew Howroyd, Nov 24 2020

Status

approved