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A157839 1728000n - 1451760. 3
276240, 2004240, 3732240, 5460240, 7188240, 8916240, 10644240, 12372240, 14100240, 15828240, 17556240, 19284240, 21012240, 22740240, 24468240, 26196240, 27924240, 29652240, 31380240, 33108240, 34836240, 36564240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as A157840(n)^2-A157838(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*(276240+1451760*x)/(x-1)^2.

MATHEMATICA

LinearRecurrence[{2, -1}, {276240, 2004240}, 40]

PROG

(MAGMA) I:=[276240, 2004240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

(PARI) a(n) = 1728000*n - 1451760.

CROSSREFS

Cf. A157838, A157840.

Sequence in context: A274351 A114664 A069372 * A237808 A271349 A162765

Adjacent sequences:  A157836 A157837 A157838 * A157840 A157841 A157842

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 07 2009

STATUS

approved

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Last modified December 5 13:38 EST 2016. Contains 278768 sequences.