A157106 a(n) = 5651522*n^2 - 2541672*n + 285769.

3395619, 17808513, 43524451, 80543433, 128865459, 188490529, 259418643, 341649801, 435184003, 540021249, 656161539, 783604873, 922351251, 1072400673, 1233753139, 1406408649, 1590367203, 1785628801, 1992193443, 2210061129

Offset: 1

Author

Vincenzo Librandi, Feb 23 2009

Keywords

• nonn
• easy

Comments

The identity (5651522*n^2-2541672*n+285769)^2-(1681*n^2-756*n+85)*(137842*n-30996)^2=1 can be written as a(n)^2-A157010(n)*A157105(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 (3,-3,1).

Crossrefs

Cf. A157010, A157105.

Programs

Magma

I:=[3395619, 17808513, 43524451]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

Maple

A157106:=n->5651522*n^2 - 2541672*n + 285769; seq(A157106(n), n=1..30); # Wesley Ivan Hurt, Jan 23 2014

Mathematica

LinearRecurrence[{3,-3,1},{3395619,17808513,43524451},30]

PARI

a(n) = 5651522*n^2 - 2541672*n + 285769

Formula

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