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.

A154376 a(n) = 25*n^2 - 2*n.

Original entry on oeis.org

23, 96, 219, 392, 615, 888, 1211, 1584, 2007, 2480, 3003, 3576, 4199, 4872, 5595, 6368, 7191, 8064, 8987, 9960, 10983, 12056, 13179, 14352, 15575, 16848, 18171, 19544, 20967, 22440, 23963, 25536, 27159, 28832, 30555, 32328, 34151, 36024
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 A154374(n)^2 - a(n)*A154378(n)^2 = 1 (see also the second comment in A154374). - Vincenzo Librandi, Jan 30 2012
The continued fraction expansion of sqrt(a(n)) is [5n-1; {1, 3, 1, 10n-2}]. - Magus K. Chu, Sep 04 2022

Links

Crossrefs

Cf. A154374, A154378.

Programs

Formula

From Vincenzo Librandi, Jan 30 2012: (Start)
G.f.: x*(23 + 27*x)/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). (End)
E.g.f.: (25*x^2 + 23*x)*exp(x). - G. C. Greubel, Sep 15 2016

A154374 a(n) = 1250*n^2 - 100*n + 1.

Original entry on oeis.org

1151, 4801, 10951, 19601, 30751, 44401, 60551, 79201, 100351, 124001, 150151, 178801, 209951, 243601, 279751, 318401, 359551, 403201, 449351, 498001, 549151, 602801, 658951, 717601, 778751, 842401, 908551, 977201, 1048351, 1122001
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 a(n)^2 - A154376(n)*A154378(n)^2 = 1. - Vincenzo Librandi, Jan 30 2012
This is the case s = 5 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Jan 30 2012

Links

Crossrefs

Cf. A154376, A154378.

Programs

  • Magma
    I:=[1151, 4801, 10951]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 30 2012
  • Mathematica
    LinearRecurrence[{3, -3, 1}, {1151, 4801, 10951}, 40] (* Vincenzo Librandi, Jan 30 2012 *)
  • PARI
    a(n)=1250*n^2-100*n+1 \\ Charles R Greathouse IV, Dec 27 2011

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 29 2012
G.f.: x*(1151 + 1348*x + x^2)/(1-x)^3. - Vincenzo Librandi, Jan 29 2012
E.g.f.: -1 + (1 + 1150*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 15 2016
Showing 1-2 of 2 results.

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

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