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A158688 a(n) = 1089*n^2 + 33. 2
33, 1122, 4389, 9834, 17457, 27258, 39237, 53394, 69729, 88242, 108933, 131802, 156849, 184074, 213477, 245058, 278817, 314754, 352869, 393162, 435633, 480282, 527109, 576114, 627297, 680658, 736197, 793914, 853809, 915882, 980133, 1046562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (66*n^2 + 1)^2 - (1089*n^2 + 33)*(2*n)^2 = 1 can be written as A158689(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.: -33*(1 + 31*x + 34*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {33, 1122, 4389}, 50] (* Vincenzo Librandi, Feb 20 2012 *)

PROG

(MAGMA) I:=[33, 1122, 4389]; [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=0, 40, print1(1089*n^2 + 33", ")); \\ Vincenzo Librandi, Feb 20 2012

CROSSREFS

Cf. A158689, A005843.

Sequence in context: A130835 A262101 A077420 * A294436 A242492 A065424

Adjacent sequences:  A158685 A158686 A158687 * A158689 A158690 A158691

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 24 2009

EXTENSIONS

Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009

STATUS

approved

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Last modified November 16 21:47 EST 2018. Contains 317275 sequences. (Running on oeis4.)