A157760 a(n) = 2809*n^2 - 1000*n + 89.

1898, 9325, 22370, 41033, 65314, 95213, 130730, 171865, 218618, 270989, 328978, 392585, 461810, 536653, 617114, 703193, 794890, 892205, 995138, 1103689, 1217858, 1337645, 1463050, 1594073, 1730714, 1872973, 2020850, 2174345

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-a(n)*A157761(n)^2=1.

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

Subsequence of A031396, see A157757.

Cf. A157761, A157762.

Programs

Magma

I:=[1898, 9325, 22370]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

Mathematica

LinearRecurrence[{3,-3,1},{1898,9325,22370},50]

PARI

a(n) = 2809*n^2 - 1000*n + 89;

Formula

G.f.: x*(1898 + 3631*x + 89*x^2)/(1 - x)^3.

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