A309022 Expansion of x * Product_{k>=0} (1 - x^(2^k) - x^(2^(k+1)) - x^(2^(k+2))).

0, 1, -1, -2, 1, -2, 2, 4, -1, -1, 2, 3, -2, 4, -4, -7, 1, -4, 1, 4, -2, 2, -3, -7, 2, 3, -4, -6, 4, -7, 7, 12, -1, 2, 4, 4, -1, 7, -4, -7, 2, 0, -2, -3, 3, -6, 7, 12, -2, 8, -3, -9, 4, -5, 6, 14, -4, -5, 7, 10, -7, 12, -12, -20, 1, -9, -2, 3, -4, -2, -4, -9, 1, 4, -7, -10, 4, -10, 7, 13, -2, 5, 0, -4, 2, -1, 3, 8, -3, -6, 6

Offset: 0

Author

Ilya Gutkovskiy, Jul 06 2019

Keywords

• sign

Crossrefs

Cf. A002487, A177219, A309019, A309020, A309021.

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).