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A158730 a(n) = 68*n^2 - 1. 2
67, 271, 611, 1087, 1699, 2447, 3331, 4351, 5507, 6799, 8227, 9791, 11491, 13327, 15299, 17407, 19651, 22031, 24547, 27199, 29987, 32911, 35971, 39167, 42499, 45967, 49571, 53311, 57187, 61199, 65347, 69631, 74051, 78607, 83299, 88127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (68*n^2 - 1)^2 - (1156*n^2 - 34)*(2*n)^2 = 1 can be written as a(n)^2 - A158729(n)*A005843(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

G.f.: x*(-67 - 70*x + x^2)/(x-1)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {67, 271, 611}, 50] (* Vincenzo Librandi, Feb 20 2012 *)

PROG

(MAGMA) I:=[67, 271, 611]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 20 2012

(PARI) for(n=1, 40, print1(68*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 20 2012

CROSSREFS

Cf. A005843, A158729.

Sequence in context: A142429 A158689 A142486 * A140731 A140855 A052164

Adjacent sequences:  A158727 A158728 A158729 * A158731 A158732 A158733

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 25 2009

EXTENSIONS

Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009

STATUS

approved

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Last modified June 21 16:32 EDT 2021. Contains 345365 sequences. (Running on oeis4.)