A157825 1728000n - 1620240.

107760, 1835760, 3563760, 5291760, 7019760, 8747760, 10475760, 12203760, 13931760, 15659760, 17387760, 19115760, 20843760, 22571760, 24299760, 26027760, 27755760, 29483760, 31211760, 32939760, 34667760, 36395760

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-A157824(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).

Formula

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

G.f.: x*(107760+1620240*x)/(x-1)^2.

Mathematica

LinearRecurrence[{2, -1}, {107760, 1835760}, 40]
1728000Range[50]-1620240  (* Harvey P. Dale, Mar 23 2011 *)

Prog

(Magma) I:=[107760, 1835760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 1728000*n - 1620240.

Crossrefs

Cf. A157824, A157826.

Sequence in context: A202404 A203882 A178284 * A205607 A205438 A102333

Adjacent sequences: A157822 A157823 A157824 * A157826 A157827 A157828

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved