cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

Original name: Single-edge stars with n edges.

Examples

			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)

Links

Crossrefs

Row sums of A339070 and A010356.
Column sums of A339071.
Cf. A002218, A010357, A322139, A338511.

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

A123534 Triangular array T(n,k) giving number of 2-connected graphs with n labeled nodes and k edges (n >= 3, n <= k <= n(n-1)/2).

Original entry on oeis.org

1, 3, 6, 1, 12, 70, 100, 45, 10, 1, 60, 720, 2445, 3535, 2697, 1335, 455, 105, 15, 1, 360, 7560, 46830, 133581, 216951, 232820, 183540, 111765, 53627, 20307, 5985, 1330, 210, 21, 1, 2520, 84000, 835800, 3940440, 10908688, 20317528
Offset: 3

Views

Author

N. J. A. Sloane, Nov 13 2006

Keywords

Examples

			Triangle begins (n >= 3, k >= n):
  n
  3 | 1;
  4 | 3, 6, 1;
  5 | 12, 70, 100, 45, 10, 1;
  6 | 60, 720, 2445, 3535, 2697, 1335, 455, 105, 15, 1;
  ...

References

  • R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.

Links

Crossrefs

Row sums give A013922.
Cf. A062734, A123527, A322139.

Programs

  • Mathematica
    row[n_] := row[n] = Module[{s}, s = (n-1)!*Log[x/InverseSeries[#, x]& @ (x*D[#, x]& @ Log[Sum[(1+y)^Binomial[k, 2]*x^k/k!, {k, 0, n}] + O[x]^(n+1) ])]; CoefficientList[Coefficient[s, x, n-1]/y^n, y]];
Table[row[n], {n, 3, 15}] // Flatten (* Jean-François Alcover, Aug 13 2019, after Andrew Howroyd *)
  • PARI
    row(n)={Vecrev((n-1)!*polcoef(log(x/serreverse(x*deriv(log(sum(k=0, n, (1 + y)^binomial(k, 2) * x^k / k!) + O(x*x^n))))), n-1)/y^n)}
{ for(n=3, 7, print(row(n))) } \\ Andrew Howroyd, Nov 30 2018

A338414 Number of labeled 3-connected graphs with n edges.

Original entry on oeis.org

1, 0, 15, 80, 493, 5730, 45790, 501690, 5747805, 66738169, 884847355, 12032825028, 174686734180, 2698980641742, 43470161714616, 739558796434277, 13161203468888236, 244555222834161480
Offset: 6

Views

Author

Andrew Howroyd, Nov 07 2020

Keywords

Comments

The initial terms of this sequence were computed from A123542.
The smallest 3-connected graph is the complete graph on 4 vertices which has 6 edges.

Crossrefs

Cf. A005644, A007100, A123542, A322139, A338511.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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