A281048 Expansion of x*(1 - x)*Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1))).

1, 0, -1, 1, -2, 1, 1, 0, -3, 1, 2, -1, 1, 0, -1, 1, -4, 1, 3, -2, 3, -1, -2, 1, 1, 0, -1, 1, -2, 1, 1, 0, -5, 1, 4, -3, 5, -2, -3, 1, 4, -1, -3, 2, -3, 1, 2, -1, 1, 0, -1, 1, -2, 1, 1, 0, -3, 1, 2, -1, 1, 0, -1, 1, -6, 1, 5, -4, 7, -3, -4, 1, 7, -2, -5, 3, -4, 1, 3, -2, 5, -1, -4, 3, -5, 2, 3, -1, -4, 1, 3, -2, 3, -1, -2, 1, 1, 0, -1, 1

Offset: 1

Author

Ilya Gutkovskiy, Feb 27 2017

Keywords

• sign

Comments

First differences of A005590.

Links

• Michael Gilleland, Some Self-Similar Integer Sequences
• Ilya Gutkovskiy, Extended graphical example
• R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences, arXiv:math/0307027 [math.CO], 2003.

Crossrefs

Cf. A005590, A070990, A182093.

Programs

Mathematica

Rest[CoefficientList[Series[x (1 - x) Product[1 + x^2^k - x^2^(k + 1), {k, 0, 15}], {x, 0, 100}], x]]
Differences[a[0] = 0; a[1] = 1; a[n_] := a[n] = If[OddQ[n], a[(n-1)/2 + 1] - a[(n-1)/2], a[n/2]]; Table[a[n], {n, 0, 100}]]

Formula

G.f.: x*(1 - x)*Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1))).