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A309048
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Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) - x^(3^(k+1))).
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4
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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
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OFFSET
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0,28
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LINKS
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FORMULA
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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).
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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