A158633 a(n) = 529*n^2 - 23.

506, 2093, 4738, 8441, 13202, 19021, 25898, 33833, 42826, 52877, 63986, 76153, 89378, 103661, 119002, 135401, 152858, 171373, 190946, 211577, 233266, 256013, 279818, 304681, 330602, 357581, 385618, 414713, 444866, 476077, 508346, 541673, 576058, 611501, 648002

Offset

1,1

Comments

The identity (46*n^2-1)^2-(529*n^2-23)*(2*n)^2 = 1 can be written as A158634(n)^2-a(n)*A005843(n)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]

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

Formula

G.f.: 23*x*(-22-25*x+x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 16 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(23))*Pi/sqrt(23))/46.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(23))*Pi/sqrt(23) - 1)/46. (End)

Maple

A158633:=n->529*n^2 - 23: seq(A158633(n), n=1..50); # Wesley Ivan Hurt, Jan 28 2017

Mathematica

a[n_] := 529*n^2 - 23; Array[a, 50] (* Amiram Eldar, Mar 16 2023 *)

Prog

(PARI) for(n=1, 40, print1(529*n^2 - 23", ")); \\ Vincenzo Librandi, Feb 17 2012

Crossrefs

Cf. A005843, A158634.

Sequence in context: A126846 A332150 A336561 * A204954 A204947 A295992

Adjacent sequences: A158630 A158631 A158632 * A158634 A158635 A158636

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 23 2009

Extensions

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

Status

approved