A157824 3600n^2 - 6751n + 3165.

14, 4063, 15312, 33761, 59410, 92259, 132308, 179557, 234006, 295655, 364504, 440553, 523802, 614251, 711900, 816749, 928798, 1048047, 1174496, 1308145, 1448994, 1597043, 1752292, 1914741, 2084390, 2261239, 2445288, 2636537

Offset

1,1

Comments

The identity (103680000*n^2-194428800*n+91152001)^2-(3600*n^2-6751*n+3165)*(1728000*n-1620240)^2=1 can be written as A157826(n)^2-a(n)*A157825(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).

Formula

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

G.f.: x*(-14-4021*x-3165*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {14, 4063, 15312}, 40]

Prog

(Magma) I:=[14, 4063, 15312]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 3600*n^2 - 6751*n + 3165.

Crossrefs

Cf. A157825, A157826.

Sequence in context: A368022 A337961 A188955 * A180588 A214441 A241326

Adjacent sequences: A157821 A157822 A157823 * A157825 A157826 A157827

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved