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A094267 First differences of A001511. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

James Spahlinger, Table of n, a(n) for n = 0..10000

FORMULA

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

EXAMPLE

G.f. = 1 - x + 2*x^2 - 2*x^3 + x^4 - x^5 + 3*x^6 - 3*x^7 + x^8 - x^9 + ...

PROG

(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 */

CROSSREFS

Absolute values give A050603. Cf. A001511, A005187.

Sequence in context: A064894 A003638 * A136480 A050603 A286554 A037162

Adjacent sequences:  A094264 A094265 A094266 * A094268 A094269 A094270

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Jun 03 2004

STATUS

approved

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Last modified February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)