A158554 a(n) = 28*n^2 - 1.

27, 111, 251, 447, 699, 1007, 1371, 1791, 2267, 2799, 3387, 4031, 4731, 5487, 6299, 7167, 8091, 9071, 10107, 11199, 12347, 13551, 14811, 16127, 17499, 18927, 20411, 21951, 23547, 25199, 26907, 28671, 30491, 32367, 34299, 36287, 38331, 40431, 42587, 44799, 47067

Offset

1,1

Comments

The identity (28*n^2 - 1)^2 - (196*n^2 - 14)*(2*n)^2 = 1 can be written as a(n)^2 - A158553(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.: x*(-27 - 30*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(28))*Pi/sqrt(28))/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(28))*Pi/sqrt(28) - 1)/2. (End)

Mathematica

28Range[50]^2-1  (* Harvey P. Dale, Mar 17 2011 *)
LinearRecurrence[{3, -3, 1}, {27, 111, 251}, 40] (* Vincenzo Librandi, Feb 14 2012 *)

Prog

(Magma) I:=[27, 111, 251]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(28*n^2-1", ")); \\ Vincenzo Librandi, Feb 14 2012

Crossrefs

Cf. A005843, A158553.

Sequence in context: A193393 A143938 A042428 * A267812 A029699 A087795

Adjacent sequences: A158551 A158552 A158553 * A158555 A158556 A158557

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Extensions

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

Status

approved