A309047 Expansion of Product_{k>=0} (1 + x^(2^k) - x^(3*2^k)).

1, 1, 1, 0, 1, 0, 0, -1, 1, 1, 0, -1, 0, 0, -1, -1, 1, 2, 1, 0, 0, -1, -1, -1, 0, 1, 0, 0, -1, -1, -1, 0, 1, 2, 2, 1, 1, -1, 0, -1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, 1, 1, 0, -1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, 1, 1, 2, 1, 2, 0, 1, -1, 1, 0, -1, -2, 0, 1, -1, -1, 0, 1, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1

Offset

0,18

Links

Table of n, a(n) for n=0..109.

Formula

G.f. A(x) satisfies: A(x) = (1 + x - x^3) * A(x^2).

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

Mathematica

nmax = 109; CoefficientList[Series[Product[(1 + x^(2^k) - x^(3 2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 109; A[_] = 1; Do[A[x_] = (1 + x - x^3) A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] - a[(n - 3)/2]]; Table[a[n], {n, 0, 109}]

Crossrefs

Cf. A002487, A005590, A120562.

Sequence in context: A354100 A118229 A172250 * A255317 A309168 A179229

Adjacent sequences: A309044 A309045 A309046 * A309048 A309049 A309050

Keyword

sign

Author

Ilya Gutkovskiy, Jul 09 2019

Status

approved