A158550 a(n) = 169*n^2 - 13.

156, 663, 1508, 2691, 4212, 6071, 8268, 10803, 13676, 16887, 20436, 24323, 28548, 33111, 38012, 43251, 48828, 54743, 60996, 67587, 74516, 81783, 89388, 97331, 105612, 114231, 123188, 132483, 142116, 152087, 162396, 173043, 184028, 195351, 207012, 219011, 231348

Offset

1,1

Comments

The identity (26*n^2 - 1)^2 - (169*n^2 - 13)*(2*n)^2 = 1 can be written as A158551(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.: 13*x*(-12 - 15*x + x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 06 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(13))*Pi/sqrt(13))/26.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(13))*Pi/sqrt(13) - 1)/26. (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {156, 663, 1508}, 40] (* Vincenzo Librandi, Feb 14 2012 *)
169*Range[40]^2-13 (* Harvey P. Dale, Apr 12 2017 *)

Prog

(Magma) I:=[156, 663, 1508]; [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(169*n^2 - 13", ")); \\ Vincenzo Librandi, Feb 14 2012

Crossrefs

Cf. A005843, A158551.

Sequence in context: A259947 A043356 A038476 * A156994 A304619 A204718

Adjacent sequences: A158547 A158548 A158549 * A158551 A158552 A158553

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Extensions

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

Status

approved