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 1-2 of 2 results.

A021031 Decimal expansion of 1/27.

Original entry on oeis.org

0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7, 0, 3, 7
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			0.037037037037037037037037037037037037037...

Links

Programs

  • Mathematica
    RealDigits[1/27, 10, 108][[1]] (* Alonso del Arte, Feb 26 2015 *)

Formula

From Bruno Berselli, Sep 24 2010: (Start)
G.f.: x*(3+7*x)/(1-x^3).
a(n) - a(n-3) = 0 for n > 2.
a(n) = A175833(n) - 4 = 4*(n-3*floor(n/3)) - (1 - (-1)^(n-3*floor((n+1)/3)))/2.
(End)

A175828 a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.

Original entry on oeis.org

1, 2, 15, 26, 53, 74, 115, 146, 201, 242, 311, 362, 445, 506, 603, 674, 785, 866, 991, 1082, 1221, 1322, 1475, 1586, 1753, 1874, 2055, 2186, 2381, 2522, 2731, 2882, 3105, 3266, 3503, 3674, 3925, 4106, 4371, 4562, 4841, 5042, 5335, 5546, 5853, 6074
Offset: 0

Views

Author

Bruno Berselli, Sep 21 2010 - Sep 25 2010

Keywords

Comments

a(n) == A068073(n) (mod 4).
a(h) == 0 (mod 11) for h = 11*(k-floor((k-1)/3))-2*(-1)^(k+floor(k/3)) (cf. A175833).

Links

Crossrefs

Cf. A068073, A010718, A142241, A175833.

Programs

  • Magma
    [(n*(6*n+1)+(n+2)*(-1)^n)/2: n in [0..50]];
  • Magma
    I:=[1,2,15,26,53]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 19 2013
  • Mathematica
    Table[(n (6 n + 1) + (n + 2) (-1)^n)/2, {n, 0, 50}]
CoefficientList[Series[(1 + x + 11 x^2 + 9 x^3 + 2 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{1,2,-2,-1,1},{1,2,15,26,53},70] (* Harvey P. Dale, Jul 03 2019 *)

Formula

G.f.: (1+x+11*x^2+9*x^3+2*x^4)/((1+x)^2*(1-x)^3).
a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>4.
a(n)-a(n-2)-(a(n-1)-a(n-3)) = 2*A010718(n-1) for n>2.
a(n)-a(n-2)+(a(n-1)-a(n-3)) = A142241(n-2) for n>2.
Showing 1-2 of 2 results.

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

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