A083037 - OEIS

%I #10 Feb 07 2013 17:15:01

%S 1,0,-1,0,1,0,1,2,1,0,1,0,-1,0,1,0,-1,0,-1,-2,-1,0,-1,0,1,0,-1,0,1,0,

%T 1,2,1,0,1,0,-1,0,1,0,1,2,1,0,1,2,1,2,3,2,1,2,1,0,1,2,1,0,1,0,-1,0,1,

%U 0,1,2,1,0,1,0,-1,0,1,0,-1,0,-1,-2,-1,0,-1,0,1,0,-1,0,1,0,1,2,1,0,1,0,-1,0,1,0,-1,0,-1,-2,-1,0,-1,0,1,0,-1,0,-1,-2,-1,0

%N a(n)=2*A083036(n)-n. Also -A123737(n).

%H Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="http://www.math.uiuc.edu/~reznick/ors.pdf">Almost alternating sums</a>, Amer. Math. Monthly, Vol. 113 (October 2006), pp. 673-688.

%F O'Bryant, Reznick, & Serbinowska show that |a(n)| <= k log n + 1, with k = 1/(2 log (1 + sqrt(2))), and further a(n) > k log n + 0.78 infinitely often. - _Charles R Greathouse IV_, Feb 07 2013

%o (PARI) a(n)=-sum(i=1, n, (-1)^sqrtint(2*i^2)) \\ _Charles R Greathouse IV_, Feb 07 2013

%Y Cf. A083035, A083036, A083038, A123737.

%K sign

%O 1,8

%A _Benoit Cloitre_, Apr 17 2003