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A157626 100n^2 - 151n + 57. 3
6, 155, 504, 1053, 1802, 2751, 3900, 5249, 6798, 8547, 10496, 12645, 14994, 17543, 20292, 23241, 26390, 29739, 33288, 37037, 40986, 45135, 49484, 54033, 58782, 63731, 68880, 74229, 79778, 85527, 91476, 97625, 103974, 110523, 117272, 124221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (80000*n^2-120800*n+45601)^2-(100*n.^2-151*n+57)*(8000*n-6040)^2=1 can be written as A157628(n)^2-a(n)*A157627(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*(-6-137*x-57*x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {6, 155, 504}, 40]

PROG

(MAGMA) I:=[6, 155, 504]; [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) = 100*n^2 - 151*n + 57.

CROSSREFS

Cf. A157627, A157628.

Sequence in context: A092122 A285368 A003460 * A229098 A203023 A128120

Adjacent sequences:  A157623 A157624 A157625 * A157627 A157628 A157629

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 03 2009

STATUS

approved

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)