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.

A157263 a(n) = 1728*n - 1320.

Original entry on oeis.org

408, 2136, 3864, 5592, 7320, 9048, 10776, 12504, 14232, 15960, 17688, 19416, 21144, 22872, 24600, 26328, 28056, 29784, 31512, 33240, 34968, 36696, 38424, 40152, 41880, 43608, 45336, 47064, 48792, 50520, 52248, 53976, 55704, 57432, 59160
Offset: 1

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Author

Vincenzo Librandi, Feb 26 2009

Keywords

Comments

The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as A157264(n)^2-A157262(n)*a(n)^2=1. - Vincenzo Librandi, Jan 27 2012

Links

Crossrefs

Cf. A157262, A157264.

Programs

  • Magma
    I:=[408, 2136]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 27 2012
  • Mathematica
    LinearRecurrence[{2,-1},{408,2136},40] (* Vincenzo Librandi, Jan 27 2012 *)
1728*Range[40]-1320 (* Harvey P. Dale, Aug 09 2012 *)
  • PARI
    for(n=1, 40, print1(1728*n - 1320", ")); \\ Vincenzo Librandi, Jan 27 2012

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 27 2012
G.f.: x*(408+1320*x)/(x-1)^2. - Vincenzo Librandi, Jan 27 2012
E.g.f.: (1728*x - 1320)*exp(x) + 1320. - G. C. Greubel, Feb 04 2018

A157264 a(n) = 10368*n^2 - 15840*n + 6049.

Original entry on oeis.org

577, 15841, 51841, 108577, 186049, 284257, 403201, 542881, 703297, 884449, 1086337, 1308961, 1552321, 1816417, 2101249, 2406817, 2733121, 3080161, 3447937, 3836449, 4245697, 4675681, 5126401, 5597857, 6090049, 6602977
Offset: 1

Views

Author

Vincenzo Librandi, Feb 26 2009

Keywords

Comments

The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as a(n)^2-A157262(n)*A157263(n)^2=1. - Vincenzo Librandi, Jan 27 2012

Links

Crossrefs

Cf. A157262, A157263.

Programs

  • Magma
    I:=[577, 15841, 51841]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012
  • Mathematica
    LinearRecurrence[{3,-3,1},{577,15841,51841},40] (* Vincenzo Librandi, Jan 27 2012 *)
Table[10368n^2-15840n+6049,{n,30}] (* Harvey P. Dale, Nov 18 2024 *)
  • PARI
    for(n=1, 40, print1(10368*n^2 - 15840*n + 6049", ")); \\ Vincenzo Librandi, Jan 27 2012

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012
G.f.: x*(-577-14110*x-6049*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012
E.g.f.: (10368*x^2 - 5472*x + 6049)*exp(x) - 6049. - G. C. Greubel, Feb 04 2018
Showing 1-2 of 2 results.

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

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