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A078027
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Expansion of (1 - x)/(1 - x^2 - x^3).
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13
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1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426
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OFFSET
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0,11
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LINKS
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FORMULA
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a(n) is asymptotic to r^(n-2) / (2*r+3) where r = 1.3247179572447..., the real root of x^3 = x + 1. For n >= 4, a(n) = a(n-2) + a(n-3). - Philippe Deléham, Jan 13 2004
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MAPLE
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seq(coeff(series((1-x)/(1-x^2-x^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 04 2019
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MATHEMATICA
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CoefficientList[Series[(1-x)/(1-x^2-x^3), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2019 *)
LinearRecurrence[{0, 1, 1}, {1, -1, 1}, 60] (* Harvey P. Dale, Jun 20 2020 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1-x^2-x^3) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1-x)/(1-x^2-x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[1, -1, 1];; for n in [4..60] do a[n]:=a[n-2]+a[n-3]; od; a; # G. C. Greubel, Aug 04 2019
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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