A309020 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, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 0, 1, 2, 2, 4, 3, 3, 2, 1, 2, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 3, 2, 3, 2, 4, 4, 5, 3, 2, 3, 2, 2, 0, 1, 1, 2, 3, 2, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, 1, 1, 4, 3, 4, 2, 2, 3, 3, 2, 3, 4, 6, 4, 5, 5, 4, 3, 0, 2

Offset: 0

Author

Ilya Gutkovskiy, Jul 06 2019

Keywords

• sign

Crossrefs

Cf. A002487, A005590, A309019, A309021, 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) + a(n+1) - a(n-1).