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.

A040110 Continued fraction for sqrt(122).

Original entry on oeis.org

11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			11 + 1/(22 + 1/(22 + 1/(22 + 1/(22 + ...)))) = sqrt(122).

Links

Crossrefs

Cf. A040000, A041220/A041221 (convergents).

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[122],300] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011*)

Formula

From Elmo R. Oliveira, Feb 11 2024: (Start)
a(n) = 22 = A010861(n) for n >= 1.
G.f.: 11*(1+x)/(1-x).
E.g.f.: 22*exp(x) - 11.
a(n) = 11*A040000(n). (End)

A141694 a(n) = 22*n + 12.

Original entry on oeis.org

12, 34, 56, 78, 100, 122, 144, 166, 188, 210, 232, 254, 276, 298, 320, 342, 364, 386, 408, 430, 452, 474, 496, 518, 540, 562, 584, 606, 628, 650, 672, 694, 716, 738, 760, 782, 804, 826, 848, 870, 892, 914, 936, 958, 980, 1002, 1024, 1046, 1068, 1090, 1112
Offset: 0

Views

Author

Paul Curtz, Sep 10 2008

Keywords

Links

Crossrefs

Cf. A008604, A010861 (first differences), A017461.

Programs

Formula

From G. C. Greubel, Jun 03 2018: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: 2*(6 + 5*x)/(1 - x)^2.
E.g.f.: 2*(6 + 11*x)*exp(x). (End)
a(n) = 2*A017461(n). - Elmo R. Oliveira, Apr 11 2025

Extensions

Edited by R. J. Mathar, Oct 24 2008
Offset changed from 1 to 0 by Vincenzo Librandi, Aug 08 2011

A023020 Number of partitions of n into parts of 22 kinds.

Original entry on oeis.org

1, 22, 275, 2530, 18975, 122430, 702328, 3661900, 17627775, 79264900, 335937954, 1351507830, 5191041625, 19125838600, 67862904725, 232671319474, 773027485065, 2494957906100, 7839428942950, 24025993453000, 71941861591215
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

a(n) is Euler transform of A010861. - Alois P. Heinz, Oct 17 2008

Links

Crossrefs

Cf. 22nd column of A144064. - Alois P. Heinz, Oct 17 2008

Programs

  • Maple
    with (numtheory): a:= proc(n) option remember; `if`(n=0, 1, add (add (d*22, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq (a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
  • Mathematica
    CoefficientList[Series[1/QPochhammer[x]^22, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)
  • PARI
    Vec(1/eta(x)^22 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Formula

G.f.: Product_{m>=1} 1/(1-x^m)^22.
a(0) = 1, a(n) = (22/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
a(n) ~ m^((m+1)/4) * exp(Pi*sqrt(2*m*n/3)) / (2^((3*m+5)/4) * 3^((m+1)/4) * n^((m+3)/4)) * (1 - ((9+Pi^2)*m^2+36*m+27) / (24*Pi*sqrt(6*m*n))), set m = 22. - Vaclav Kotesovec, Jun 28 2025
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.