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URL: https://oeis.org/A138231

⇱ A138231 - OEIS

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A138231
A009545 alternated with its first differences.
2
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
0,5
COMMENTS
The unsigned sequence contains 3 copies of the strictly positive powers of 2.
FORMULA
a(2n) = A009545(n). a(2n+1) = A009545(n+1)-A009545(n) = (-1)^(n+1)*A009116(n).
a(n) = 2*a(n-2)-2*a(n-4). a(n) = -4*a(n-8), n > 7.
O.g.f.: x*(1+x-x^2)/(1-2*x^2+2*x^4). - R. J. Mathar, Jul 08 2008
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, May 05 2008
EXTENSIONS
Edited by R. J. Mathar, Jul 08 2008
STATUS
approved