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Search: id:A111113
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| A111113 |
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a(2^m) = 1, a(2^m+1) = -1 (m>0), otherwise a(n) = 0. |
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+0
2
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| 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, 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, -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
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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A. G. Postnikov, Tauberian Theory and Its Applications, Proc. Steklov. Inst. Math., 144 (1979), translated as Issue 2, 1980. See p. 29.
A. Renyi, On a Tauberian theorem of O. Szasz, Acta Univ. Szeged. Sect. Sci. Math., 11 (1946), 119-123.
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FORMULA
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Euler transform of A079559 is sequence offset -1. - Michael Somos Aug 03 2009
G.f.: (1 - x) * (Sum_{k>0} x^(2^k)). - Michael Somos Aug 03 2009
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EXAMPLE
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x^2 - x^3 + x^4 - x^5 + x^8 - x^9 + x^16 - x^17 + x^32 - x^33 + ...
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PROGRAM
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(PARI) {a(n) = if( n<2, 0, [1, -1, 0] [1 + min(2, n - 2^(length(binary(n)) - 1))] )} /* Michael Somos Aug 03 2009 */
(PARI) {a(n) = if( n<2, 0, if( n%2, -a(n - 1), n == 2^valuation(n, 2)))} /* Michael Somos Aug 03 2009 */
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CROSSREFS
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Sequence in context: A073089 A011657 A072126 this_sequence A095190 A131735 A131736
Adjacent sequences: A111110 A111111 A111112 this_sequence A111114 A111115 A111116
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 15 2005
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