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A158604 a(n) = 42*n^2 + 1. 3
1, 43, 169, 379, 673, 1051, 1513, 2059, 2689, 3403, 4201, 5083, 6049, 7099, 8233, 9451, 10753, 12139, 13609, 15163, 16801, 18523, 20329, 22219, 24193, 26251, 28393, 30619, 32929, 35323, 37801, 40363, 43009, 45739, 48553, 51451, 54433, 57499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (42*n^2 + 1)^2 - (441*n^2 + 21)*(2*n)^2 = 1 can be written as a(n)^2 - A158603(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: -(1 + 40*x + 43*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 43, 169}, 50] (* Vincenzo Librandi, Feb 16 2012 *)

PROG

(MAGMA) I:=[1, 43, 169]; [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 16 2012

(PARI) for(n=0, 40, print1(42*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 16 2012

CROSSREFS

Cf. A005843, A158603.

Sequence in context: A142016 A140640 A083357 * A057816 A162295 A187722

Adjacent sequences:  A158601 A158602 A158603 * A158605 A158606 A158607

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 22 2009

EXTENSIONS

Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009

STATUS

approved

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Last modified October 16 03:27 EDT 2019. Contains 328039 sequences. (Running on oeis4.)