A138232 First differences of A138231.

1, 0, 0, 1, -2, 2, -4, 2, -4, 0, 0, -4, 8, -8, 16, -8, 16, 0, 0, 16, -32, 32, -64, 32, -64, 0, 0, -64, 128, -128, 256, -128, 256, 0, 0, 256, -512, 512, -1024, 512, -1024, 0, 0, -1024, 2048, -2048, 4096, -2048, 4096, 0, 0, 4096, -8192, 8192, -16384, 8192, -16384, 0, 0, -16384, 32768

Offset

0,5

Comments

The sequence contains 2 copies of 1 and 3 copies of the higher powers 2^j (up to sign).

Links

Table of n, a(n) for n=0..60.

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

Formula

a(n) = 2a(n-2)-2a(n-4). a(n) = -4a(n-8).

a(2n) = (-1)^(n+1)*A090132(n). a(2n+1) = A009545(n).

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

Mathematica

LinearRecurrence[{0, 2, 0, -2}, {1, 0, 0, 1}, 70] (* Harvey P. Dale, Apr 23 2022 *)

Crossrefs

Cf. A000079, A131577.

Sequence in context: A138785 A131817 A214430 * A248913 A227951 A102641

Adjacent sequences: A138229 A138230 A138231 * A138233 A138234 A138235

Keyword

sign

Author

Paul Curtz, May 05 2008

Extensions

Edited by R. J. Mathar, Jul 08 2008

Status

approved