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.

A154377 a(n) = 25*n^2 + 2*n.

Original entry on oeis.org

27, 104, 231, 408, 635, 912, 1239, 1616, 2043, 2520, 3047, 3624, 4251, 4928, 5655, 6432, 7259, 8136, 9063, 10040, 11067, 12144, 13271, 14448, 15675, 16952, 18279, 19656, 21083, 22560, 24087, 25664, 27291, 28968, 30695, 32472, 34299, 36176
Offset: 1

Views

Author

Vincenzo Librandi, Jan 08 2009

Keywords

Comments

The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - a(n)*A154379(n)^2 = 1 (see also the second comment in A154375). - Vincenzo Librandi, Jan 30 2012
The continued fraction expansion of sqrt(4*a(n)) is [10n; {2, 1, 1, 5n-1, 1, 1, 2, 20n}]. - Magus K. Chu, Sep 27 2022

Links

Crossrefs

Cf. A154375, A154379.

Programs

  • Mathematica
    LinearRecurrence[{3,-3,1},{27,104,231},50]
  • PARI
    a(n)=25*n^2+2*n \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(27 + 23*x)/(1-x)^3.
E.g.f.: (25*x^2 + 27*x)*exp(x). - G. C. Greubel, Sep 15 2016

A154379 a(n) = 250*n + 10.

Original entry on oeis.org

260, 510, 760, 1010, 1260, 1510, 1760, 2010, 2260, 2510, 2760, 3010, 3260, 3510, 3760, 4010, 4260, 4510, 4760, 5010, 5260, 5510, 5760, 6010, 6260, 6510, 6760, 7010, 7260, 7510, 7760, 8010, 8260, 8510, 8760, 9010, 9260, 9510, 9760, 10010, 10260
Offset: 1

Views

Author

Vincenzo Librandi, Jan 08 2009

Keywords

Comments

The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - A154377(n)*a(n)^2 = 1 (see also the second comment in A154375). - Vincenzo Librandi, Jan 30 2012

Links

Crossrefs

Cf. A154375, A154377.

Programs

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 30 2012
G.f.: 10*x*(26 - x)/(1-x)^2. - Vincenzo Librandi, Jan 30 2012 [corrected by Georg Fischer, May 12 2019]
E.g.f.: 10*( (25*x + 1)*exp(x) - 1). - G. C. Greubel, Sep 15 2016

Extensions

Definition corrected by Paolo P. Lava, Jan 14 2009
Showing 1-2 of 2 results.

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