A158667 a(n) = 841*n^2 - 29.

812, 3335, 7540, 13427, 20996, 30247, 41180, 53795, 68092, 84071, 101732, 121075, 142100, 164807, 189196, 215267, 243020, 272455, 303572, 336371, 370852, 407015, 444860, 484387, 525596, 568487, 613060, 659315, 707252, 756871, 808172, 861155, 915820, 972167, 1030196

Offset

1,1

Comments

The identity (58*n^2-1)^2 - (841*n^2-29)*(2*n)^2 = 1 can be written as A158668(n)^2 - a(n)*A005843(n)^2 = 1.

Links

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

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

Formula

G.f.: 29*x*(-28-31*x+x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 20 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(29))*Pi/sqrt(29))/58.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(29))*Pi/sqrt(29) - 1)/58. (End)

Maple

A158667:=n->841*n^2 - 29; seq(A158667(k), k=1..50); # Wesley Ivan Hurt, Nov 01 2013

Mathematica

LinearRecurrence[{3, -3, 1}, {812, 3335, 7540}, 40] (* or *) 29 (29 Range[40]^2 - 1) (* Harvey P. Dale, Oct 31 2011 *)

Prog

(Magma) I:=[812, 3335, 7540]; [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 18 2012
(PARI) for(n=1, 40, print1(841*n^2-29", ")); \\ Vincenzo Librandi, Feb 18 2012

Crossrefs

Cf. A005843, A158668.

Sequence in context: A093633 A045228 A252223 * A035854 A099116 A183820

Adjacent sequences: A158664 A158665 A158666 * A158668 A158669 A158670

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 24 2009

Extensions

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

Status

approved