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A157854 1728000n - 384240. 3
1343760, 3071760, 4799760, 6527760, 8255760, 9983760, 11711760, 13439760, 15167760, 16895760, 18623760, 20351760, 22079760, 23807760, 25535760, 27263760, 28991760, 30719760, 32447760, 34175760, 35903760, 37631760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (103680000*n^2-46108800*n+5126401)^2-(3600*n^2-1601*n +178)*(1728000*n-384240)^2=1 can be written as A157855(n)^2-A157853(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*(1343760+384240*x)/(x-1)^2.

MATHEMATICA

LinearRecurrence[{2, -1}, {1343760, 3071760}, 40]

PROG

(Magma) I:=[1343760, 3071760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

(PARI) a(n) = 1728000*n - 384240.

CROSSREFS

Cf, A157853, A157855.

Sequence in context: A214291 A023047 A206254 * A234727 A184661 A187961

Adjacent sequences: A157851 A157852 A157853 * A157855 A157856 A157857

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 08 2009

STATUS

approved

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Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)