A111113 - OEIS

%I #17 Apr 06 2018 10:33:34

%S 0,0,1,-1,1,-1,0,0,1,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,

%U -1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(2^m) = 1, a(2^m+1) = -1 (m>0), otherwise a(n) = 0.

%H A. G. Postnikov, <a href="http://mi.mathnet.ru/eng/tm2540">Tauberian Theory and Its Applications</a>, Proc. Steklov. Inst. Math., 144 (1979), translated as Issue 2, 1980. See p. 29.

%H A. Renyi, <a href="http://acta.fyx.hu/acta/showCustomerArticle.action?id=5859&amp;dataObjectType=article&amp;returnAction=showCustomerVolume&amp;sessionDataSetId=35b1e983238aa90&amp;style=">On a Tauberian theorem of O. Szasz</a>, Acta Univ. Szeged. Sect. Sci. Math., 11 (1946), 119-123.

%F Euler transform of A079559 is sequence offset -1. - _Michael Somos_, Aug 03 2009

%F G.f.: (1 - x) * (Sum_{k>0} x^(2^k)). - _Michael Somos_, Aug 03 2009

%F |a(n)| = A001683(n)(mod 2) for n > 1. - _John M. Campbell_, Apr 01 2018

%e G.f. = x^2 - x^3 + x^4 - x^5 + x^8 - x^9 + x^16 - x^17 + x^32 - x^33 + ...

%o (PARI) {a(n) = if( n<2, 0, [1, -1, 0] [1 + min(2, n - 2^(length(binary(n)) - 1))] )} /* _Michael Somos_, Aug 03 2009 */

%o (PARI) {a(n) = if( n<2, 0, if( n%2, -a(n - 1), n == 2^valuation(n, 2)))} /* _Michael Somos_, Aug 03 2009 */

%K sign

%O 0,1

%A _N. J. A. Sloane_, Oct 15 2005