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.

A171408 a(n) = A171373(n+1) - 2*A171373(n).

Original entry on oeis.org

4, 4, 4, 4, 0, -12, -32, -52, -52, 0, 136, 356, 576, 576, 0, -1508, -3948, -6388, -6388, 0, 16724, 43784, 70844, 70844, 0, -185472, -485572, -785672, -785672, 0, 2056916, 5385076, 8713236, 8713236, 0, -22811548, -59721408, -96631268, -96631268, 0, 252983944, 662320564
Offset: 0

Views

Author

Paul Curtz, Dec 08 2009

Keywords

Comments

The least significant digits have a period of length 20. Another period (not the same but of the same length, as this a sequence contains negative numbers) is defined reading the sequence modulo 10.

Links

Crossrefs

Cf. A138112, A105371.

Formula

a(n)=4*A105371(n-1), n>0.
a(n)= 3*a(n-1) -4*a(n-2) +2*a(n-3) -a(n-4). G.f.: 4*(1-2*x+2*x^2)/(1-3*x+4*x^2-2*x^3+x^4).

Extensions

Edited and extended by R. J. Mathar, Mar 02 2010

A171372 a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 1.

Original entry on oeis.org

1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5
Offset: 0

Views

Author

Paul Curtz, Dec 07 2009

Keywords

Comments

The diagonal of a table of numerators of the Rydberg-Ritz spectrum of hydrogen:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... A000012
0, 5, 3, 21, 2, 45, 15, 77, 6, 117, 35, ... A061037
0, 9, 5, 33, 3, 65, 21, 105, 1, 153, 45, ... A061041
0, 13, 7, 5, 4, 85, 1, 133, 10, 7, 55, ... A061045
0, 17, 9, 57, 5, 105, 33, 161, 3, 225, 65, ... A061049
0, 21, 11, 69, 6, 1, 39, 189, 14, 261, 3, ...
0, 25, 13, 1, 7, 145, 5, 217, 1, 11, 85, ...
0, 29, 15, 93, 8, 165, 51, 5, 18, 333, 95, ...
0, 33, 17, 105, 9, 185, 57, 273, 5, 369, 105, ...
0, 37, 19, 13, 10, 205, 7, 301, 22, 5, 115, ...
0, 41, 21, 129, 11, 9, 69, 329, 3, 441, 1, ...
In that respect, constructed similar to A144437.

Links

Crossrefs

Cf. A171373 (binomial transform), A171408, A105371.

Programs

  • Magma
    [1] cat [Numerator(5/(6*n)^2): n in [1..100]]; // G. C. Greubel, Sep 20 2018
  • Mathematica
    Table[If[n==0,1,Numerator[5/(6*n)^2]], {n,0,100}] (* G. C. Greubel, Sep 20 2018 *)
  • PARI
    concat([1], vector(100, n, numerator(5/(6*n)^2))) \\ G. C. Greubel, Sep 20 2018

Formula

a(n) = numerator of 5/(6*n)^2 .
Period 5: repeat [1,5,5,5,5].
G.f.: (1 + 5*x + 5*x^2 + 5*x^3 + 5*x^4)/((1-x)*(1 + x + x^2 + x^3 + x^4)).
a(n) = 1 + 4*sign(n mod 5). - Wesley Ivan Hurt, Sep 26 2018
a(n) = (21-8*cos(2*n*Pi/5)-8*cos(4*n*Pi/5))/5. - Wesley Ivan Hurt, Sep 27 2018

Extensions

Edited by R. J. Mathar, Dec 15 2009
Showing 1-2 of 2 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.