A114569 a(n) = 9*4^n - 1.

8, 35, 143, 575, 2303, 9215, 36863, 147455, 589823, 2359295, 9437183, 37748735, 150994943, 603979775, 2415919103, 9663676415, 38654705663, 154618822655, 618475290623, 2473901162495, 9895604649983, 39582418599935

Offset

0,1

Comments

Squares of the cotangents of the arcsins of 1/(3*2^n).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5, -4).

Formula

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 4*a(n-1) + 3, n>0; a(0)=8.

a(n) = 5*a(n-1) - 4*a(n-2), n>1; a(0)=8, a(1)=35.

G.f.: (8-5*x)/(1-5*x+4*x^2). (End)

Example

a(2) = 143.

Mathematica

Table[(9*4^n) - 1, {n, 0, 23}] (* Stefan Steinerberger, Feb 16 2006 *)

Prog

(Magma) [9*4^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 29 2011

Crossrefs

Cf. A024036, A097743, A156760.

Sequence in context: A094616 A318020 A340522 * A189599 A302078 A320405

Adjacent sequences: A114566 A114567 A114568 * A114570 A114571 A114572

Keyword

easy,nonn

Author

Al Hakanson (hawkuu(AT)excite.com), Feb 16 2006

Extensions

More terms from Stefan Steinerberger, Feb 16 2006

Status

approved