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A157732 388962n^2 - 430416n + 119071. 3
77617, 814087, 2328481, 4620799, 7691041, 11539207, 16165297, 21569311, 27751249, 34711111, 42448897, 50964607, 60258241, 70329799, 81179281, 92806687, 105212017, 118395271, 132356449, 147095551, 162612577, 178907527 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (388962*n^2-430416*n+119071)^2-(441*n^2-488*n+135)*(18522*n-10248)^2=1 can be written as a(n)^2-A157730(n)*A157731(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*(-77617-581236*x-119071*x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {77617, 814087, 2328481}, 40]

PROG

(MAGMA) I:=[77617, 814087, 2328481]; [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) = 388962*n^2 - 430416*n + 119071.

CROSSREFS

Cf. A157730, A157731.

Sequence in context: A206275 A249958 A232349 * A210123 A069044 A250012

Adjacent sequences:  A157729 A157730 A157731 * A157733 A157734 A157735

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 05 2009

STATUS

approved

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Last modified December 10 23:13 EST 2016. Contains 279021 sequences.