A097581 a(n) = 3*2^floor((n-1)/2) + (-1)^n.

2, 4, 5, 7, 11, 13, 23, 25, 47, 49, 95, 97, 191, 193, 383, 385, 767, 769, 1535, 1537, 3071, 3073, 6143, 6145, 12287, 12289, 24575, 24577, 49151, 49153, 98303, 98305, 196607, 196609, 393215, 393217, 786431, 786433, 1572863, 1572865

Offset: 1

Author

Pierre CAMI, Sep 20 2004

Keywords

• nonn

Comments

Previous name was: a(1)=2 then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1.

This sequence a(n)=A016116(n-1)+A086341(n). Generalization: starting with a(1) even then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1 you get a new sequence as a(1) increases. But if a(1) is odd, you get always the same sequence with only less values as a(1) increases. If a(1) is even, the sequence difference between two sequences with different but consecutive a(1) is the sequence of powers of 2 = 2,2,4,4,8,8,16,16,32,32,......

Examples

			Starting with a(1)=4 the new sequence is 4,6,9,11,19,21,39,41,79,81,159,161
The sequence difference between sequence starting with a(1)=4 and the sequence starting with a(1)=2 is 2,2,4,4,8,8,16,16,32,32,64,64,.......
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2,2).

Crossrefs

Cf. A016116, A086341.

Programs

Mathematica

LinearRecurrence[{-1,2,2},{2,4,5},40] (* Harvey P. Dale, Aug 10 2011 *)
Table[3*2^(Floor[(n - 1)/2]) + (-1)^n, {n, 1,50}] (* G. C. Greubel, Apr 18 2017 *)

PARI

a(n)=3*2^floor((n-1)/2)+(-1)^n

Formula

From R. J. Mathar, Nov 13 2009: (Start)

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

G.f.: x*(2+6*x+5*x^2)/((1+x)*(1-2*x^2)). (End)

Extensions

Equation in the comment corrected by R. J. Mathar, Nov 13 2009

Better name from Ralf Stephan, Aug 19 2013