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, 158329674399743, 633318697598975, 2533274790395903

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

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

Examples

			a(2) = 143.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A024036, A097743, A156760, A199208.

Programs

Magma

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

Mathematica

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

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)

From Elmo R. Oliveira, May 08 2025: (Start)

E.g.f.: exp(x)*(9*exp(3*x) - 1).

a(n) = A199208(n) - 2. (End)

Extensions

More terms from Stefan Steinerberger, Feb 16 2006