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.

A058297 Continued fraction for Wallis' number (A007493).

Original entry on oeis.org

2, 10, 1, 1, 2, 1, 3, 1, 1, 12, 3, 5, 1, 1, 2, 1, 6, 1, 11, 4, 42, 1, 2, 1, 1, 1, 1, 1, 2, 1, 16, 1, 1, 1, 1, 6, 2, 5, 22, 6, 31, 2, 1, 4, 17, 2, 1, 5, 2, 4, 5, 2, 74, 45, 1, 24, 3, 1, 13, 1, 18, 2, 8, 1, 1, 5, 2, 1, 1, 2, 10, 1, 6, 6, 1, 1, 7, 21, 1, 1, 2, 2, 8, 3, 2, 2, 4, 9, 7, 4, 106, 3, 2, 1, 3, 2
Offset: 0

Views

Author

Robert G. Wilson v, Dec 07 2000

Keywords

Comments

The real solution to the equation x^3 - 2x - 5 = 0.

Examples

			2.09455148154232659148238654... = 2 + 1/(10 + 1/(1 + 1/(1 + 1/(2 + ...))))

References

  • David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 27.

Links

Crossrefs

Cf. A007493.

Programs

  • Mathematica
    ContinuedFraction[ 1/3*(135/2 - (3*Sqrt[1929])/2)^(1/3) + (1/2*(45 + Sqrt[1929]))^(1/3) / 3^(2/3), 100]
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=NULL; p=x^3 - 2*x - 5; rs=polroots(p); r=real(rs[1]); c=contfrac(r); for (n=1, 20001, write("b058297.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 03 2009
  • PARI
    contfrac(polrootsreal(x^3-2*x-5)[1]) \\ Charles R Greathouse IV, Apr 14 2014

A107248 a(n) = 4*a(n-2) - 4*a(n-4) + 25*a(n-6).

Original entry on oeis.org

1, 1, 1, 37, 37, 169, 169, 553, 553, 2461, 2461, 11857, 11857, 51409, 51409, 219733, 219733, 969721, 969721, 4285177, 4285177, 18755149, 18755149, 82122913, 82122913, 360600481, 360600481, 1582788997, 1582788997, 6941826889
Offset: 0

Views

Author

Roger L. Bagula, Jun 08 2005

Keywords

Links

Crossrefs

Cf. A007493.

Programs

  • Magma
    I:=[1,1,1,37,37,169]; [n le 6 select I[n] else 4*Self(n-2)-4*Self(n-4)+25*Self(n-6): n in [1..40]]; // Vincenzo Librandi, Feb 21 2018
  • Mathematica
    CoefficientList[Series[-(1 + x - 3 x^2 + 33 x^3 + 37 x^4 + 25 x^5)/((5 x^3 - 2 x^2 + 1) (5 x^3 + 2 x^2 - 1)), {x, 0, 29}], x] (* Michael De Vlieger, Feb 20 2018 *)
LinearRecurrence[{0, 4, 0, -4, 0, 25}, {1, 1, 1, 37, 37, 169}, 30] (* Vincenzo Librandi, Feb 21 2018 *)

Formula

From R. J. Mathar, Jul 03 2009: (Start)
a(n) = 4*a(n-2) - 4*a(n-4) + 25*a(n-6).
G.f.: -(1+x-3*x^2+33*x^3+37*x^4+25*x^5)/((5*x^3-2*x^2+1)*(5*x^3+2*x^2-1)).
(End)

Extensions

Edited by N. J. A. Sloane, May 13 2006
New name using Mathar's recurrence from Joerg Arndt, Feb 20 2018

A107229 a(n) = 2*a(n-2)+5*a(n-3), n>6.

Original entry on oeis.org

1, 1, 1, 3, 3, 11, 9, 7, 73, 59, 181, 483, 657, 1871, 3729, 7027, 16813, 32699, 68761, 149463, 301017, 642731, 1349349, 2790547, 5912353, 12327839, 25777441, 54217443, 113194077, 237322091, 497475369, 1040614567, 2181561193
Offset: 0

Views

Author

Roger L. Bagula, Jun 08 2005

Keywords

Links

Crossrefs

Cf. A007493.

Programs

  • Mathematica
    F[1] = 1; F[2] = 1; F[3] = 1; F[n__] := F[n] = 2*F[n - 2] - 5*F[n - 3] b = Table[Abs[F[n]], {n, 1, 50}]
LinearRecurrence[{0,2,5},{1,1,1,3,3,11,9,7},40] (* Harvey P. Dale, Jun 10 2019 *)

Formula

G.f.: 6*x^4+2*x+(x^2+x-1)/(-1+2*x^2+5*x^3). [Sep 28 2009]

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
Showing 1-3 of 3 results.

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