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 1-4 of 4 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

A339160 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 3, 6, 3, 1, 0, 1, 4, 11, 11, 4, 1, 0, 1, 5, 22, 33, 23, 5, 1, 0, 1, 7, 38, 89, 96, 40, 7, 1, 0, 1, 8, 63, 212, 345, 234, 70, 8, 1, 0, 1, 10, 98, 463, 1083, 1146, 546, 110, 10, 1, 0, 1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0
Offset: 1

Views

Author

Andrew Howroyd, Dec 05 2020

Keywords

Examples

			Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
  1;
  1,  0;
  1,  1,   0;
  1,  1,   1,   0;
  1,  2,   2,   1,    0;
  1,  3,   6,   3,    1,    0;
  1,  4,  11,  11,    4,    1,    0;
  1,  5,  22,  33,   23,    5,    1,    0;
  1,  7,  38,  89,   96,   40,    7,    1,   0;
  1,  8,  63, 212,  345,  234,   70,    8,   1,  0;
  1, 10,  98, 463, 1083, 1146,  546,  110,  10,  1, 0;
  1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0;
  ...

Links

Crossrefs

Column k=3 is A001399(n-3).
Row sums are A010357.
Cf. A046752, A191646, A339070.

Formula

T(n,2) = T(n,n) = 1.

A360881 Number of unlabeled nonseparable (or 2-connected) multigraphs with n edges, loops allowed.

Original entry on oeis.org

1, 2, 5, 9, 19, 44, 111, 328, 1090, 3988, 15838, 67295, 301417, 1412821, 6882398, 34682721, 180170661, 962288228, 5273162329
Offset: 1

Views

Author

Andrew Howroyd, Feb 25 2023

Keywords

Crossrefs

Row sums of A360880.
Cf. A007717, A007719, A010357.

A363240 Number of distinct resistances that can be produced from a circuit that is a 2-connected loopless multigraph with n edges and each edge having a unit resistor.

Original entry on oeis.org

1, 2, 5, 12, 32, 88, 260, 819, 2680, 8642, 27976, 88946, 281541, 893028, 2841344, 9092174, 29176634, 93854841, 302611365
Offset: 2

Views

Author

Zhao Hui Du, May 23 2023

Keywords

Comments

The resistances between any two nodes of the graph are counted.
All resistances in A337517 can be obtained by serial combinations of resistances of one or more 2-connected loopless multigraphs.

Examples

			a(2)=1 since the only multigraph with 2 edges is a double edge graph which forms resistance 1/2.
For n=4, there are a quadruple edge graph (resistance 1/4), a triangle graph with one double edge (2/5 between double edge and 3/5 between single edge) and square graph (3/4 between neighbor nodes and 1 between opposite nodes) so a(4)=5.

Crossrefs

Cf. A010357, A337517.
Showing 1-4 of 4 results.

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

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