A133730 Alternating sign sequence A033999 interleaved with Jacobsthal sequence A001045.

1, 0, -1, 1, 1, 1, -1, 3, 1, 5, -1, 11, 1, 21, -1, 43, 1, 85, -1, 171, 1, 341, -1, 683, 1, 1365, -1, 2731, 1, 5461, -1, 10923, 1, 21845, -1, 43691, 1, 87381, -1, 174763, 1, 349525, -1, 699051, 1, 1398101, -1, 2796203, 1, 5592405, -1, 11184811, 1, 22369621, -1, 44739243, 1

Offset: 0

Author

Paul Curtz, Jan 04 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

Crossrefs

Cf. A033999, A001045, A133684.

Programs

Mathematica

LinearRecurrence[{0,1,0,2},{1,0,-1,1},70] (* Harvey P. Dale, Sep 04 2024 *)

Formula

From R. J. Mathar, Jan 09 2008 (Start):

a(2n) = (-1)^n. a(2n+1) = A001045(n).

O.g.f.: -(x-1)*(x^2-x-1)/[(2*x^2-1)*(1+x^2)].

a(n) = A133684(n+1)-A133684(n).

First differences: a(2n)-a(2n+1) = -2*A001045(n-2) for n>=3; a(2n+1)-a(2n) = 4*A001045(n-2) for n >=2. (End)

Extensions

Edited by R. J. Mathar, Jan 09 2008

Definition amended by Georg Fischer, Nov 02 2021