A157803 - OEIS

A157803

a(n) = 8984250*n - 8464830.

519420, 9503670, 18487920, 27472170, 36456420, 45440670, 54424920, 63409170, 72393420, 81377670, 90361920, 99346170, 108330420, 117314670, 126298920, 135283170, 144267420, 153251670, 162235920, 171220170, 180204420, 189188670

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OFFSET

1,1

COMMENTS

The identity (1482401250*n^2-2793393900*n+1315947601)^2-(27225*n^2-51302*n+24168)*(8984250*n-8464830)^2=1 can be written as A157804(n)^2-A157802(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).

FORMULA

From Harvey P. Dale, Nov 01 2011: (Start)

a(1) = 519420, a(2)=9503670; for n>2, a(n) = 2*a(n-1) - a(n-2).

G.f.: 330*x*(25651*x + 1574)/(x-1)^2. (End)

MATHEMATICA

8984250 Range[30] - 8464830 (* or *) LinearRecurrence[{2, -1}, {519420, 9503670}, 30] (* Harvey P. Dale, Nov 01 2011 *)

PROG

(Magma) I:=[519420, 9503670]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

(PARI) a(n) = 8984250*n - 8464830;