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A158603 a(n) = 441*n^2 + 21. 2
21, 462, 1785, 3990, 7077, 11046, 15897, 21630, 28245, 35742, 44121, 53382, 63525, 74550, 86457, 99246, 112917, 127470, 142905, 159222, 176421, 194502, 213465, 233310, 254037, 275646, 298137, 321510, 345765, 370902, 396921, 423822, 451605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (42*n^2 + 1)^2 - (441*n^2 + 21)*(2*n)^2 = 1 can be written as A158604(n)^2 - a(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.: -21*(1 + 19*x + 22*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {21, 462, 1785}, 50] (* Vincenzo Librandi, Feb 16 2012 *)

PROG

(MAGMA) I:=[21, 462, 1785]; [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(441*n^2 + 21", ")); \\ Vincenzo Librandi, Feb 16 2012

CROSSREFS

Cf. A005843, A158604.

Sequence in context: A157014 A076552 A126996 * A307600 A025603 A296586

Adjacent sequences:  A158600 A158601 A158602 * A158604 A158605 A158606

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 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)