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 1-8 of 8 results.

A006799 Number of vertex-transitive graphs with n nodes.

Original entry on oeis.org

1, 2, 2, 4, 3, 8, 4, 14, 9, 22, 8, 74, 14, 56, 48, 286, 36, 380, 60, 1214, 240, 816, 188, 15506, 464, 4236, 1434, 25850, 1182, 46308, 2192, 677402, 6768, 132580, 11150, 1963202, 14602, 814216, 48462, 13104170, 52488, 9462226, 99880, 39134640, 399420, 34333800, 364724
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.
  • Brendan McKay, personal communication.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Row sums of A319367.
Cf. A006792, A006793, A006800, A185959.

Formula

Inverse Moebius transform of A006800. - Andrew Howroyd, Sep 18 2018

Extensions

More terms from Vladeta Jovovic, Jun 30 2007
a(32)-a(47) from Danny Rorabaugh, Nov 26 2018

A319368 Triangle read by rows: T(n,k) is the number of simple connected vertex transitive graphs with n nodes and valency k, (0 <= k < n).

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 3, 2, 1, 1, 0, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 1, 3, 3, 4, 3, 2, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 1, 4, 10, 12, 13, 11, 7, 4, 1, 1, 0, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1
Offset: 1

Views

Author

Andrew Howroyd, Sep 17 2018

Keywords

Examples

			Triangle begins:
  1;
  0, 1;
  0, 0, 1;
  0, 0, 1, 1;
  0, 0, 1, 0,  1;
  0, 0, 1, 2,  1,  1;
  0, 0, 1, 0,  1,  0,  1;
  0, 0, 1, 2,  3,  2,  1,  1;
  0, 0, 1, 0,  3,  0,  2,  0,  1;
  0, 0, 1, 3,  3,  4,  3,  2,  1,  1;
  0, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
  0, 0, 1, 4, 10, 12, 13, 11,  7,  4,  1,  1;
  0, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
  0, 0, 1, 3,  5,  6,  8,  9,  6,  6,  3,  2,  1,  1;
  0, 0, 1, 0,  7,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
  0, 0, 1, 4, 13, 25, 39, 47, 48, 40, 27, 16,  7,  3, 1, 1;
  0, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
  0, 0, 1, 5, 12, 23, 36, 45, 53, 54, 45, 38, 24, 16, 7, 4, 1, 1;
  ...

Links

Crossrefs

Row sums are A006800.
Cf. A319367.

Formula

T(n,k) = Sum_{d|n} moebius(n/d) * A319367(d,k).

A319372 Triangle read by rows: T(n,k) is the number of Cayley graphs with n nodes and valency k, (0 <= k < n).

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 0, 2, 0, 3, 0, 2, 0, 1, 1, 1, 2, 2, 4, 4, 2, 2, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 1, 4, 7, 11, 13, 13, 11, 7, 4, 1, 1, 1, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1
Offset: 1

Views

Author

Andrew Howroyd, Sep 17 2018

Keywords

Comments

First differs from A319367 in row 10.

Examples

			Triangle begins, n >= 1, 0 <= k < n:
  1;
  1, 1;
  1, 0, 1;
  1, 1, 1, 1;
  1, 0, 1, 0,  1;
  1, 1, 2, 2,  1,  1;
  1, 0, 1, 0,  1,  0,  1;
  1, 1, 2, 3,  3,  2,  1,  1;
  1, 0, 2, 0,  3,  0,  2,  0,  1;
  1, 1, 2, 2,  4,  4,  2,  2,  1,  1;
  1, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
  1, 1, 4, 7, 11, 13, 13, 11,  7,  4,  1,  1;
  1, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
  1, 1, 2, 3,  6,  6,  9,  9,  6,  6,  3,  2,  1,  1;
  1, 0, 3, 0,  7,  0, 11,  0, 11,  0,  7,  0,  3,  0, 1;
  1, 1, 3, 7, 15, 26, 39, 47, 47, 39, 26, 15,  7,  3, 1, 1;
  1, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
  1, 1, 4, 7, 16, 23, 38, 45, 53, 53, 45, 38, 23, 16, 7, 4, 1, 1;
  ...

Links

Crossrefs

Column k=3 is aerated A319374.
Row sums are A185959.
Cf. A319367, A319368.

A023646 Number of vertex-transitive graphs of valency 3 with 2n nodes.

Original entry on oeis.org

1, 2, 3, 3, 7, 3, 7, 7, 11, 3, 20, 5, 10, 15
Offset: 2

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.

Crossrefs

Even-indexed terms of column k=3 of A319367.

Extensions

a(14)-a(15) added by Andrew Howroyd, Sep 18 2018

A023647 Number of vertex-transitive graphs of valency 4 with n nodes.

Original entry on oeis.org

1, 1, 1, 3, 3, 4, 2, 11, 3, 6, 8, 16, 4, 16, 4, 28, 11, 11, 5, 74, 9, 16, 16, 34, 7, 52, 7
Offset: 5

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.

Crossrefs

Column k=4 of A319367.

Extensions

a(27)-a(31) added by Andrew Howroyd, Sep 18 2018

A023640 Number of vertex-transitive graphs of valency 5 with 2n nodes.

Original entry on oeis.org

1, 2, 4, 13, 6, 27, 24, 47, 18, 167, 29, 79, 105
Offset: 3

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.

Crossrefs

Even-indexed terms of column k=5 of A319367.

A023641 Number of vertex-transitive graphs of valency 6 with n nodes.

Original entry on oeis.org

1, 1, 2, 3, 2, 13, 4, 9, 12, 40, 7, 38, 10, 83, 29, 38, 15, 373, 25, 71, 54, 204, 26, 259, 31
Offset: 7

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.

Crossrefs

Column k=6 of A319367.

Extensions

a(27)-a(31) added by Andrew Howroyd, Sep 18 2018

A023643 Number of vertex-transitive graphs of valency 8 with n nodes.

Original entry on oeis.org

1, 1, 1, 7, 3, 6, 12, 48, 10, 54, 14, 149, 48, 79, 30, 1064, 57, 204, 128, 748, 73, 935, 91
Offset: 9

Views

Author

N. J. A. Sloane

Keywords

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 649.

Crossrefs

Column k=8 of A319367.

Extensions

a(27)-a(31) added by Andrew Howroyd, Sep 18 2018
Showing 1-8 of 8 results.

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

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