login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158668 a(n) = 58*n^2 - 1. 2
57, 231, 521, 927, 1449, 2087, 2841, 3711, 4697, 5799, 7017, 8351, 9801, 11367, 13049, 14847, 16761, 18791, 20937, 23199, 25577, 28071, 30681, 33407, 36249, 39207, 42281, 45471, 48777, 52199, 55737, 59391, 63161, 67047, 71049, 75167 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (58*n^2 - 1)^2 - (841*n^2 - 29)*(2*n)^2 = 1 can be written as a(n)^2 - A158667(n)*A005843(n)^2 = 1.

LINKS

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

Vincenzo Librandi, X^2-AY^2=1

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

FORMULA

G.f.: x*(-57 - 60*x + x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {57, 231, 521}, 50] (* Vincenzo Librandi, Feb 18 2012 *)

PROG

(MAGMA) I:=[57, 231, 521]; [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(58*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 18 2012

CROSSREFS

Cf. A005843, A158667.

Sequence in context: A336191 A277805 A158660 * A145296 A176635 A048422

Adjacent sequences:  A158665 A158666 A158667 * A158669 A158670 A158671

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 12:30 EDT 2022. Contains 355986 sequences. (Running on oeis4.)