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A157010 1681n^2 - 756n + 85. 3
1010, 5297, 12946, 23957, 38330, 56065, 77162, 101621, 129442, 160625, 195170, 233077, 274346, 318977, 366970, 418325, 473042, 531121, 592562, 657365, 725530, 797057, 871946, 950197, 1031810, 1116785, 1205122, 1296821, 1391882, 1490305 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (5651522*n^2-2541672*n+285769)^2-(1681*n^2-756*n+85)*(137842*n-30996)^2=1 can be written as (A157106(n))^2-(a(n))*(A157105(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*(-1010-2267*x-85*x^2)/(x-1)^3.

MAPLE

A157010:=n->1681*n^2 - 756*n + 85; seq(A157010(n), n=1..30); # Wesley Ivan Hurt, Jan 24 2014

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1010, 5297, 12946}, 30]

PROG

(MAGMA) I:=[1010, 5297, 12946]; [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) = 1681*n^2 - 756*n + 85.

CROSSREFS

Cf. A157105, A157106.

Sequence in context: A286138 A145808 A252683 * A076940 A173521 A266442

Adjacent sequences:  A157007 A157008 A157009 * A157011 A157012 A157013

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 23 2009

STATUS

approved

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.