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 1-6 of 6 results.

A002004 Davenport-Schinzel numbers of degree 4 on n symbols.

Original entry on oeis.org

1, 4, 8, 12, 17, 22, 27, 32, 37, 42, 47, 53, 58, 64, 69, 75, 81, 86, 92, 98, 104
Offset: 1

Views

Author

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • D. P. Roselle and R. G. Stanton, Results on Davenport-Schinzel sequences, pp. 249-267 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.

Crossrefs

A column of array in A259874.

Extensions

Title improved by Sean A. Irvine, Feb 19 2016

A005004 Davenport-Schinzel numbers of degree n on 3 symbols.

Original entry on oeis.org

1, 3, 5, 8, 10, 14, 16, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 92, 94, 98, 100, 104, 106, 110, 112, 116, 118, 122, 124, 128, 130, 134, 136, 140, 142, 146, 148, 152, 154, 158, 160, 164, 166
Offset: 1

Views

Author

Keywords

References

  • Annette J. Dobson and Shiela Oates Macdonald, "Lower bounds for the lengths of Davenport-Schinzel sequences", Utilitas Mathematica 6 (1974): 251-257.
  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.

Crossrefs

Cf. A002004.
A row of the array in A259874.

Programs

  • Maple
    A005004:=(z**3-z**2+z+1)*(z**2+z+1)/(1+z)/(z-1)**2; # Conjectured by Simon Plouffe in his 1992 dissertation
  • Mathematica
    Join[{1, 3, 5}, LinearRecurrence[{1, 1, -1}, {8, 10, 14}, 60]] (* Jean-François Alcover, Sep 04 2018 *)

Formula

For n > 3, a(2*n) = 6 * n - 4 and a(2*n+1) = 6 * n - 5. - Sean A. Irvine, Feb 19 2016

Extensions

Improved title and more terms from Sean A. Irvine, Feb 19 2016

A005281 Davenport-Schinzel numbers of degree 6 on n symbols.

Original entry on oeis.org

1, 6, 14, 23, 34, 46
Offset: 1

Views

Author

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • D. P. Roselle and R. G. Stanton, Results on Davenport-Schinzel sequences, pp. 249-267 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Extensions

Name edited by Jinyuan Wang, Aug 09 2021
a(6) from Fausto A. C. Cariboni, Dec 01 2022

A005005 Davenport-Schinzel numbers of degree n on 4 symbols.

Original entry on oeis.org

1, 4, 7, 12, 16, 23, 28, 35, 40, 47, 52, 59, 64, 71, 76, 83, 88, 95, 100, 107, 112, 119, 124, 131, 136, 143, 148, 155, 160, 167, 172, 179, 184, 191, 196, 203, 208, 215, 220, 227, 232, 239, 244, 251, 256, 263, 268, 275, 280, 287, 292, 299, 304
Offset: 1

Views

Author

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.

Crossrefs

A row of the array in A259874.

Programs

  • Mathematica
    LinearRecurrence[{1,1,-1},{1,4,7,12,16,23,28},60] (* Harvey P. Dale, Jul 22 2021 *)

Formula

For n > 4, a(2*n) = 12 * n - 13 and a(2*n+1) = 12 * n - 14. - Sean A. Irvine, Feb 19 2016
From Chai Wah Wu, Jun 17 2020: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 7.
G.f.: x*(x^2 + x + 1)*(x^4 + x^3 - x^2 + 2*x + 1)/((x - 1)^2*(x + 1)). (End)

Extensions

Title improved and more terms from Sean A. Irvine, Feb 19 2016

A005006 Davenport-Schinzel numbers of degree n on 5 symbols.

Original entry on oeis.org

1, 5, 9, 17, 22, 34, 41, 53, 61, 73
Offset: 1

Views

Author

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.

Crossrefs

A row of the array in A259874.

Extensions

Title improved by Sean A. Irvine, Feb 19 2016

A005280 Davenport-Schinzel numbers of degree 5 on n symbols.

Original entry on oeis.org

1, 5, 10, 16, 22, 29
Offset: 1

Views

Author

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E20.
  • D. P. Roselle and R. G. Stanton, Results on Davenport-Schinzel sequences, pp. 249-267 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Extensions

Name edited by Jinyuan Wang, Aug 09 2021
Showing 1-6 of 6 results.