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A094267
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First differences of A001511.
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5
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1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 4, -4, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 5, -5, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 4, -4, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 6, -6, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 4, -4, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 2, -2, 1, -1, 5, -5, 1, -1, 2, -2, 1, -1, 3, -3
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OFFSET
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0,3
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COMMENTS
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For n even, sum_{k=1..n} a(k) > 0. For n odd, sum_{k=1..n} a(k) = 0. - James Spahlinger, Oct 13 2013
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LINKS
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James Spahlinger, Table of n, a(n) for n = 0..10000
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FORMULA
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a(n) = (-1)^n * A050603(n).
G.f.: -1/x + (1 - x)*Sum_{k>=0} x^(2^k-2)/(1 - x^(2^k)). - Ilya Gutkovskiy, Feb 28 2017
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EXAMPLE
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G.f. = 1 - x + 2*x^2 - 2*x^3 + x^4 - x^5 + 3*x^6 - 3*x^7 + x^8 - x^9 + ...
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PROG
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(PARI) a(n)=(-1)^n*valuation(n+2-n%2, 2) \\ Charles R Greathouse IV, Oct 14 2013
(PARI) {a(n) = my(A); if( n<0, 0, A = sum(k=0, length( binary(n+2)) - 1, x^(2^k) / (1 - x^(2^k)), x^3 * O(x^n)); polcoeff( (A * (1 - x) - x) / x^2, n))}; /* Michael Somos, May 11 2014 */
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CROSSREFS
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Absolute values give A050603. Cf. A001511, A005187.
Sequence in context: A152805 A064894 A003638 * A136480 A050603 A286554
Adjacent sequences: A094264 A094265 A094266 * A094268 A094269 A094270
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Jun 03 2004
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STATUS
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approved
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