A157761 a(n) = 297754*n - 53000.

244754, 542508, 840262, 1138016, 1435770, 1733524, 2031278, 2329032, 2626786, 2924540, 3222294, 3520048, 3817802, 4115556, 4413310, 4711064, 5008818, 5306572, 5604326, 5902080, 6199834, 6497588, 6795342, 7093096, 7390850

Offset: 1

Author

Vincenzo Librandi, Mar 06 2009

Keywords

• nonn
• easy

Comments

The identity (15780962*n^2-5618000*n+500001)^2-(2809*n^2-1000*n+89)*(297754*n-53000)^2=1 can be written as A157762(n)^2-A157760(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. A157760, A157762.

Programs

Magma

I:=[244754, 542508]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2, -1}, {244754, 542508}, 50]

PARI

a(n) = 297754n - 53000;

Formula

a(n) = 2*a(n-1) - a(n-2) = 3*a(n-1) - 3*a(n-2) + a(n-3).

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