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A309048 Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) - x^(3^(k+1))). 4
1, 1, 1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 1, 1, 1, 0, 1, 1, -1, 0, 0, 1, 1, 1, 0, 1, 1, -2, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 1, 1, 1, 0, 1, 1, -2, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 1, 1, 1, 0, 1, 1, -3, -2, -2, 1, -1, -1, 0, -1, -1, 2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,28

LINKS

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

FORMULA

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

a(0) = 1; a(3*n) = a(n) - a(n-1), a(3*n+1) = a(n), a(3*n+2) = a(n).

MATHEMATICA

nmax = 109; CoefficientList[Series[Product[(1 + x^(3^k) + x^(2 3^k) - x^(3^(k + 1))), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

nmax = 109; A[_] = 1; Do[A[x_] = (1 + x + x^2 - x^3) A[x^3] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := Switch[Mod[n, 3], 0, a[n/3] - a[(n - 3)/3], 1, a[(n - 1)/3], 2, a[(n - 2)/3]]; Table[a[n], {n, 0, 109}]

CROSSREFS

Cf. A005590, A054390, A309047.

Sequence in context: A316867 A127327 A321144 * A086072 A086009 A086010

Adjacent sequences:  A309045 A309046 A309047 * A309049 A309050 A309051

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 09 2019

STATUS

approved

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Last modified September 26 14:45 EDT 2021. Contains 347668 sequences. (Running on oeis4.)