A157363 a(n) = 686*n - 14.

672, 1358, 2044, 2730, 3416, 4102, 4788, 5474, 6160, 6846, 7532, 8218, 8904, 9590, 10276, 10962, 11648, 12334, 13020, 13706, 14392, 15078, 15764, 16450, 17136, 17822, 18508, 19194, 19880, 20566, 21252, 21938, 22624, 23310, 23996, 24682

Offset: 1

Author

Vincenzo Librandi, Feb 28 2009

Keywords

• nonn
• easy

Comments

The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as A157364(n)^2-A157362(n)*a(n)^2=1.

Links

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

Crossrefs

Cf. A157362, A157364.

Programs

Magma

I:=[672, 1358]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

Mathematica

LinearRecurrence[{2,-1},{672,1358},50]

PARI

a(n) = 686*n-14

Formula

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

G.f.: 14*x*(48+x)/(1-x)^2.

E.g.f.: 14*(1 - (1-49*x)*exp(x)). - G. C. Greubel, Feb 02 2018