A339068 -id:A339068 - cp's OEIS frontend

A006289 Number of series-reduced 2-connected graphs with n nodes.

1, 3, 19, 149, 2581, 84151, 5201856, 577050233, 113372069299, 39618015318982, 24916462761069296, 28563626972509456884, 60366734349116636660402, 237406975840304068884168139, 1750330441810569047176394509086

Offset: 4

N. J. A. Sloane

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andrew Howroyd, Table of n, a(n) for n = 4..25
R. W. Robinson, Tables
R. W. Robinson, Tables [Local copy, with permission]
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. See also.
T. R. S. Walsh, Counting unlabeled three-connected and homeomorphically irreducible two-connected graphs, J. Combin. Theory Ser. B 32 (1982), no. 1, 12-32.

Row sums of A339069.

Cf. A006290, A339068.

Robinson and Walsh list first 25 terms.

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

Original entry on oeis.org

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

Andrew Howroyd, Nov 24 2020

			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 ...
  ...

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.

Row sums are A006289.
Column sums are A339068.
Cf. A123545, A123546, A339071, A339072.

cp's OEIS Frontend

A006289 Number of series-reduced 2-connected graphs with n nodes.

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

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cp's OEIS Frontend

A006289 Number of series-reduced 2-connected graphs with n nodes.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

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

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