A309021 Expansion of x * Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1)) - x^(2^(k+2))).

0, 1, 1, 0, 1, -2, 0, 0, 1, -3, -2, 1, 0, 2, 0, 1, 1, -4, -3, 0, -2, 6, 1, 1, 0, 1, 2, -2, 0, -1, 1, 0, 1, -6, -4, 0, -3, 7, 0, 1, -2, 8, 6, -3, 1, -6, 1, -2, 0, 0, 1, 1, 2, -5, -2, 0, 0, 1, -1, 2, 1, 0, 0, 0, 1, -7, -6, 1, -4, 10, 0, 1, -3, 10, 7, -4, 0, -6, 1, -3, -2, 9, 8, 0, 6, -17, -3, -2, 1, -4, -6

Offset: 0

Author

Ilya Gutkovskiy, Jul 06 2019

Keywords

• sign

Crossrefs

Cf. A002487, A005590, A309019, A309020, A309022.

Programs

Mathematica

nmax = 90; CoefficientList[Series[x Product[(1 + x^(2^k) - x^(2^(k + 1)) - x^(2^(k + 2))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n + 1)/2] - a[(n - 1)/2] - a[(n - 3)/2]]; Table[a[n], {n, 0, 90}]

Formula

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