A138231 A009545 alternated with its first differences.

0, 1, 1, 1, 2, 0, 2, -2, 0, -4, -4, -4, -8, 0, -8, 8, 0, 16, 16, 16, 32, 0, 32, -32, 0, -64, -64, -64, -128, 0, -128, 128, 0, 256, 256, 256, 512, 0, 512, -512, 0, -1024, -1024, -1024, -2048, 0, -2048, 2048, 0, 4096, 4096, 4096, 8192, 0, 8192, -8192, 0, -16384, -16384

Offset: 0

Author

Paul Curtz, May 05 2008

Keywords

• sign

Comments

The unsigned sequence contains 3 copies of the strictly positive powers of 2.

Links

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

Crossrefs

Cf. A000079.

Programs

Mathematica

With[{c=LinearRecurrence[{2,-2},{0,1},40]},Riffle[c,Differences[c]]] (* or *) LinearRecurrence[{0,2,0,-2},{0,1,1,1},80] (* Harvey P. Dale, Oct 15 2017 *)

Formula

a(2n)= A009545(n). a(2n+1)= A009545(n+1)-A009545(n) = (-1)^(n+1)*A009116(n).

a(n) = 2a(n-2)-2a(n-4). a(n) = -4a(n-8), n > 7.

O.g.f.: x(1+x-x^2)/(1-2x^2+2x^4). - R. J. Mathar, Jul 08 2008

Extensions

Edited by R. J. Mathar, Jul 08 2008