login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158590 a(n) = 324*n^2 + 18. 2
18, 342, 1314, 2934, 5202, 8118, 11682, 15894, 20754, 26262, 32418, 39222, 46674, 54774, 63522, 72918, 82962, 93654, 104994, 116982, 129618, 142902, 156834, 171414, 186642, 202518, 219042, 236214, 254034, 272502, 291618, 311382, 331794 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (36*n^2 + 1)^2 - (324*n^2 + 18)*(2*n)^2 = 1 can be written as A158591(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.: -18*(1 + 16*x + 19*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {18, 342, 1314}, 50] (* Vincenzo Librandi, Feb 16 2012 *)

324 Range[0, 40]^2+18 (* Harvey P. Dale, Nov 22 2018 *)

PROG

(MAGMA) I:=[18, 342, 1314]; [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 16 2012

(PARI) for(n=0, 40, print1(324*n^2 + 18", ")); \\ Vincenzo Librandi, Feb 16 2012

CROSSREFS

Cf. A005843, A158591.

Sequence in context: A068771 A039646 A212669 * A143168 A127585 A230348

Adjacent sequences:  A158587 A158588 A158589 * A158591 A158592 A158593

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 22 2009

EXTENSIONS

Comment rewritten, formula replaced by R. J. Mathar, Oct 28 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 14:47 EDT 2020. Contains 334684 sequences. (Running on oeis4.)