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A177219 a(1) = 1; a(2n) = -a(n); a(2n+1) = -a(n) + a(n+1). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..80.

J.P. Allouche and M. Mendes France, Stern-Brocot polynomials and power series, arXiv preprint arXiv:1202.0211 [math.NT], 2012. - From N. J. A. Sloane, May 10 2012

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

EXAMPLE

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

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 *)

CROSSREFS

Sequence in context: A241915 A301891 A332089 * A277700 A140191 A317840

Adjacent sequences:  A177216 A177217 A177218 * A177220 A177221 A177222

KEYWORD

sign,easy

AUTHOR

Gary W. Adamson, May 04 2010

STATUS

approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)