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A158629 a(n) = 484*n^2 + 22. 2
22, 506, 1958, 4378, 7766, 12122, 17446, 23738, 30998, 39226, 48422, 58586, 69718, 81818, 94886, 108922, 123926, 139898, 156838, 174746, 193622, 213466, 234278, 256058, 278806, 302522, 327206, 352858, 379478, 407066, 435622, 465146, 495638 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (44*n^2 + 1)^2 - (484*n^2 + 22)*(2*n)^2 = 1 can be written as A158630(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.: -22*(1 + 20*x + 23*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {22, 506, 1958}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(Magma) I:=[22, 506, 1958]; [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 17 2012

(PARI) for(n=0, 40, print1(484*n^2 + 22", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A158630.

Sequence in context: A230350 A180780 A121904 * A253777 A266884 A182610

Adjacent sequences: A158626 A158627 A158628 * A158630 A158631 A158632

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 23 2009

EXTENSIONS

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

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)