A158559 a(n) = 225*n^2 - 15.

210, 885, 2010, 3585, 5610, 8085, 11010, 14385, 18210, 22485, 27210, 32385, 38010, 44085, 50610, 57585, 65010, 72885, 81210, 89985, 99210, 108885, 119010, 129585, 140610, 152085, 164010, 176385, 189210, 202485, 216210, 230385, 245010, 260085, 275610, 291585, 308010

Offset

1,1

Comments

The identity (30*n^2 - 1)^2 - (225*n^2 - 15) * (2*n)^2 = 1 can be written as A158560(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.: 15*x*(-14 - 17*x + x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 09 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(15))*Pi/sqrt(15))/30.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(15))*Pi/sqrt(15) - 1)/30. (End)

Mathematica

15(15Range[40]^2-1) (* or *) LinearRecurrence[{3, -3, 1}, {210, 885, 2010}, 40] (* Harvey P. Dale, Jan 24 2012 *)

Prog

(Magma) I:=[210, 885, 2010]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(225*n^2 - 15", ")); \\ Vincenzo Librandi, Feb 05 2012

Crossrefs

Cf. A005843, A158560.

Sequence in context: A118279 A163263 A009127 * A235248 A235241 A046302

Adjacent sequences: A158556 A158557 A158558 * A158560 A158561 A158562

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Extensions

Comment rewritten by R. J. Mathar, Oct 16 2009

Status

approved