A177219 a(1) = 1; a(2n) = -a(n); a(2n+1) = -a(n) + a(n+1).

1, -1, -2, 1, -1, 2, 3, -1, -2, 1, 3, -2, 1, -3, -4, 1, -1, 2, 3, -1, 2, -3, -5, 2, 3, -1, -4, 3, -1, 4, 5, -1, -2, 1, 3, -2, 1, -3, -4, 1, 3, -2, -5, 3, -2, 5, 7, -2, 1, -3, -4, 1, -3, 4, 7, -3, -4, 1, 5, -4, 1, -5, -6, 1, -1, 2, 3, -1, 2, -3, -5, 2, 3, -1, -4, 3, -1, 4, 5, -1

Offset: 1

Author

Gary W. Adamson, May 04 2010

Keywords

• sign
• easy

Examples

			a(6) = 2 = (-1)*a(3) = (-1)*(-2). a(7) = 3 = (-1)*a(3) + a(4) = (-1)*(-2) + 1.
		

Links

• J.-P. Allouche and M. Mendès France, Stern-Brocot polynomials and power series, arXiv preprint arXiv:1202.0211 [math.NT], 2012. - From _N. J. A. Sloane_, May 10 2012

Programs

Maple

A177219 := proc(n)
    local npr ;
    npr := floor(n/2) ;
    if n = 1 then
        1;
    elif type(n,'even') then
        -procname(npr) ;
    else
        -procname(npr)+procname(npr+1) ;
    end if;
end proc: # R. J. Mathar, Mar 14 2014

Mathematica

a[1] = 1; a[n_] := a[n] = If[EvenQ[n], -a[n/2], -a[(n-1)/2]+a[(n-1)/2+1]];
Array[a, 80] (* Jean-François Alcover, Nov 24 2017 *)

Formula

Let M = an infinite lower triangular matrix with (1, -1, -1, 0, 0, 0,...) in every column, shifted down twice for columns k >1. Then the sequence is the left-shifted vector of Lim_{n->inf} M^n.

G.f.: x*Product_{k>=0} (1 - x^(2^k) - x^(2^(k + 1))). - Ilya Gutkovskiy, Aug 30 2017