A309790 G.f. A(x) satisfies: A(x) = 2*x*(1 - x)*A(x^2) + x/(1 - x).

0, 1, 1, 3, -1, 3, -1, 7, -5, -1, 3, 7, -5, -1, 3, 15, -13, -9, 11, -1, 3, 7, -5, 15, -13, -9, 11, -1, 3, 7, -5, 31, -29, -25, 27, -17, 19, 23, -21, -1, 3, 7, -5, 15, -13, -9, 11, 31, -29, -25, 27, -17, 19, 23, -21, -1, 3, 7, -5, 15, -13, -9, 11, 63, -61, -57, 59

Offset: 0

Author

Ilya Gutkovskiy, Aug 28 2019

Keywords

• sign
• look
• hear

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65534
• Ilya Gutkovskiy, Scatter plot of a(n) up to n=1000

Crossrefs

Cf. A000225 (fixed points), A006257.

Compare also to the scatter plots of A117966, A317825.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0, 2*
     `if`(irem(n, 2, 'r')=0, -a(r-1), a(r))+1)
    end:
seq(a(n), n=0..2^7-2);  # Alois P. Heinz, Aug 29 2019

Mathematica

nmax = 66; A[] = 0; Do[A[x] = 2 x (1 - x) A[x^2] + x/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[n_] := If[EvenQ[n], -2 a[(n - 2)/2] + 1, 2 a[(n - 1)/2] + 1]; Table[a[n], {n, 0, 66}]

Formula

a(0) = 0; a(2*n+2) = -2*a(n) + 1, a(2*n+1) = 2*a(n) + 1.