A135541 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3), with a(0) = 2, a(1) = 2.

0, 2, 7, 12, 21, 44, 91, 180, 357, 716, 1435, 2868, 5733, 11468, 22939, 45876, 91749, 183500, 367003, 734004, 1468005, 2936012, 5872027, 11744052, 23488101, 46976204, 93952411, 187904820, 375809637, 751619276, 1503238555, 3006477108

Offset: 0

Author

Paul Curtz, Feb 22 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,2).

Crossrefs

Cf. A007909, A007910, A010712, A016029, A134658.

Programs

Magma

I:=[0, 2, 7]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

Mathematica

LinearRecurrence[{2,-1,2},{0,2,7},40] (* Vincenzo Librandi, Jun 17 2012 *)

Formula

From R. J. Mathar, Feb 23 2008: (Start)

O.g.f.: -7/(5*(2x-1)) - (4x+7)/(5*(x^2+1)).

a(n) = (7*2^n - (-1)^floor(n/2)*A010712(n+1))/5. (End)

E.g.f.: (1/5)*(7*cosh(2*x) + 7*sinh(2*x) - 7*cos(x) - 4*sin(x)). - G. C. Greubel, Oct 18 2016

Extensions

More terms from R. J. Mathar, Feb 23 2008