A010355 Number of unlabeled nonseparable (or 2-connected) graphs (or blocks) with n edges.

1, 0, 1, 1, 2, 4, 7, 16, 42, 111, 331, 1094, 3829, 14380, 57069, 237188, 1027929, 4622588, 21494274, 103077677, 508743475, 2579847563, 13422868110, 71570635306, 390670937143

Offset

1,5

Comments

Original name: Single-edge stars with n edges.

Links

Table of n, a(n) for n=1..25.

George A. Baker Jr. and John M. Kincaid, The continuous-spin Ising model, g0:phi4:d field theory and the renormalization group. J. Statist. Phys. 24 (1981), no. 3, 469-528.

Brendan McKay and Adolfo Piperno, Practical Graph Isomorphism, II, Journal of Symbolic Computation, 60 (2014), pp. 94-112.

Brendan McKay and Adolfo Piperno, nauty and Traces, programs for computing automorphism groups of graphs and digraphs.

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

M. F. Sykes, D. S. McKenzie, and B. R. Heap, Specific heat of a three-dimensional Ising ferromagnet above the Curie temperature. III. The star cluster expansion, J. Phys. A: Math. Nucl. Gen., 7 (1974), 1576.

Example

From Andrew Howroyd, Nov 23 2020: (Start)
The a(1) = 1 graph is the single edge (K_2 = P_2).
The a(3) = 1 graph is the triangle (K_3).
The a(4) = 1 graph is the square (C_4).
The a(5) = 2 graphs are the cycle C_5 and a cycle of 4 nodes with one diagonal added.
(End)

Crossrefs

Row sums of A339070 and A010356.

Column sums of A339071.

Cf. A002218, A010357, A322139, A338511.

Sequence in context: A360885 A343869 A137568 * A171880 A171874 A113878

Adjacent sequences: A010352 A010353 A010354 * A010356 A010357 A010358

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(11)-a(12) from Andrey Zabolotskiy, Oct 03 2017

Name changed by Andrew Howroyd, Nov 23 2020

a(13)-a(18) added using data from Robinson's tables by Andrew Howroyd, Nov 23 2020

a(19)-a(22) from Hugo Pfoertner using program geng from nauty, Dec 04 2020

a(23)-a(24) from Hugo Pfoertner, Dec 07 2020

a(25) from Hugo Pfoertner, Jan 04 2021

Status

approved