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

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

Offset: 1

Author

Vincenzo Librandi, Feb 23 2009

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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