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.

A157111 a(n) = 137842*n - 106846.

Original entry on oeis.org

30996, 168838, 306680, 444522, 582364, 720206, 858048, 995890, 1133732, 1271574, 1409416, 1547258, 1685100, 1822942, 1960784, 2098626, 2236468, 2374310, 2512152, 2649994, 2787836, 2925678, 3063520, 3201362, 3339204, 3477046
Offset: 1

Views

Author

Vincenzo Librandi, Feb 23 2009

Keywords

Comments

The identity (5651522*n^2 - 8761372*n + 3395619)^2 - (1681*n^2 - 2606*n + 1010)*(137842*n - 106846)^2 = 1 can be written as A157112(n)^2 - A157110(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

Links

Crossrefs

Cf. A157110, A157112.

Programs

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 25 2012
G.f.: x*(106846*x + 30996)/(x-1)^2. - Vincenzo Librandi, Jan 25 2012

A157112 a(n) = 5651522*n^2 - 8761372*n + 3395619.

Original entry on oeis.org

285769, 8478963, 27975201, 58774483, 100876809, 154282179, 218990593, 295002051, 382316553, 480934099, 590854689, 712078323, 844605001, 988434723, 1143567489, 1310003299, 1487742153, 1676784051, 1877128993, 2088776979, 2311728009
Offset: 1

Views

Author

Vincenzo Librandi, Feb 23 2009

Keywords

Comments

The identity (5651522*n^2 - 8761372*n + 3395619)^2 - (1681*n^2 - 2606*n + 1010)*(137842*n - 106846)^2 = 1 can be written as a(n)^2 - A157110(n)*A157111(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

Links

Crossrefs

Cf. A157110, A157111.

Programs

  • Magma
    I:=[285769, 8478963, 27975201]; [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 25 2012
  • Mathematica
    LinearRecurrence[{3,-3,1},{285769,8478963,27975201},40] (* Vincenzo Librandi, Jan 25 2012 *)
  • PARI
    for(n=1, 22, print1(5651522*n^2 - 8761372*n + 3395619", ")); \\ Vincenzo Librandi, Jan 25 2012

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 25 2012
G.f.: x*(-285769 - 7621656*x - 3395619*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012
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.