A157758 a(n) = 297754*n - 244754.

53000, 350754, 648508, 946262, 1244016, 1541770, 1839524, 2137278, 2435032, 2732786, 3030540, 3328294, 3626048, 3923802, 4221556, 4519310, 4817064, 5114818, 5412572, 5710326, 6008080, 6305834, 6603588, 6901342, 7199096

Offset: 1

Author

Vincenzo Librandi, Mar 06 2009

Keywords

• nonn
• easy

Comments

The identity (15780962*n^2-25943924*n+10662963)^2-(2809*n^2-4618*n+1898)*(297754*n-244754)^2=1 can be written as A157759(n)^2-A157757(n)*a(n)^2=1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A157757, A157759.

Programs

Magma

I:=[53000, 350754]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

Mathematica

LinearRecurrence[{2, -1}, {53000, 350754}, 30]

PARI

a(n) = 297754*n - 244754;

Formula

a(n) = 2*a(n-1) - a(n-2).

G.f.: x*(53000 + 244754*x)/(1-x)^2.