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A339422
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G.f.: 1 / (1 + Sum_{k>=0} x^(2^k)).
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3
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1, -1, 0, 1, -2, 2, 0, -3, 4, -2, -2, 6, -6, 0, 8, -11, 4, 10, -20, 14, 10, -36, 38, -2, -54, 84, -46, -56, 152, -144, -8, 221, -316, 146, 244, -570, 482, 120, -876, 1110, -350, -1108, 2138, -1520, -896, 3548, -3914, 566, 4906, -8068, 4714, 4864, -14080, 13652, 466, -20656
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OFFSET
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0,5
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COMMENTS
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The difference between the number of compositions (ordered partitions) of n into an even number of powers of 2 and the number of compositions (ordered partitions) of n into an odd number of powers of 2.
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = A(x^2) / (1 + x * A(x^2)).
a(0) = 1; a(n) = -Sum_{k=1..n} A209229(k) * a(n-k).
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MAPLE
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b:= proc(n, t) option remember; `if`(n=0, t,
add(b(n-2^i, -t), i=0..ilog2(n)))
end:
a:= n-> b(n, 1):
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MATHEMATICA
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nmax = 55; CoefficientList[Series[1/(1 + Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[If[IntegerQ[Log[2, k]], 1, 0] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]
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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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