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

1,1

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,......

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).

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)

Example

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,.......

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 *)

Prog

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

Crossrefs

Cf. A016116, A086341.

Sequence in context: A307872 A239510 A039673 * A090614 A171022 A097697

Adjacent sequences: A097578 A097579 A097580 * A097582 A097583 A097584

Keyword

nonn

Author

Pierre CAMI, Sep 20 2004

Extensions

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

Better name from Ralf Stephan, Aug 19 2013

Status

approved