A083037 a(n)=2*A083036(n)-n. Also -A123737(n).

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, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 2, 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, 0, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, 0

Offset: 1

Author

Benoit Cloitre, Apr 17 2003

Keywords

• sign

Links

• Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, Almost alternating sums, Amer. Math. Monthly, Vol. 113 (October 2006), pp. 673-688.

Crossrefs

Cf. A083035, A083036, A083038, A123737.

Programs

PARI

a(n)=-sum(i=1, n, (-1)^sqrtint(2*i^2)) \\ Charles R Greathouse IV, Feb 07 2013

Formula

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