A157853 - OEIS

A157853

3600n^2 - 1601n + 178.

2177, 11376, 27775, 51374, 82173, 120172, 165371, 217770, 277369, 344168, 418167, 499366, 587765, 683364, 786163, 896162, 1013361, 1137760, 1269359, 1408158, 1554157, 1707356, 1867755, 2035354, 2210153, 2392152, 2581351, 2777750

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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-a(n)*A157854(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*(-2177-4845*x-178*x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {2177, 11376, 27775}, 40]

PROG

(Magma) I:=[2177, 11376, 27775]; [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 - 1601*n + 178.

CROSSREFS

Cf. A157854, A157855.

Sequence in context: A170776 A250240 A157476 * A072141 A008918 A262792

Adjacent sequences: A157850 A157851 A157852 * A157854 A157855 A157856

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 08 2009

STATUS

approved