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A123891
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Expansion of (1-3*x^2+x^3)/(1-3*x+x^3).
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2
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1, 3, 6, 18, 51, 147, 423, 1218, 3507, 10098, 29076, 83721, 241065, 694119, 1998636, 5754843, 16570410, 47712594, 137382939, 395578407, 1139022627, 3279684942, 9443476419, 27191406630, 78294534948, 225440128425, 649128978645, 1869092400987, 5381837074536
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OFFSET
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0,2
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REFERENCES
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A. Burstein and T. Mansour, Words restricted by 3-letter ..., Annals. Combin., 7 (2003), 1-14.
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LINKS
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FORMULA
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MAPLE
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seq(coeff(series((1-3*x^2+x^3)/(1-3*x+x^3), x, n+1), x, n), n = 0..40); # G. C. Greubel, Aug 07 2019
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MATHEMATICA
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CoefficientList[Series[(1-3x^2+x^3)/(1-3x+x^3), {x, 0, 40}], x] (* Harvey P. Dale, Jan 16 2022 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1-3*x^2+x^3)/(1-3*x+x^3)) \\ G. C. Greubel, Aug 07 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-3*x^2+x^3)/(1-3*x+x^3) )); // G. C. Greubel, Aug 07 2019
(Sage) ((1-3*x^2+x^3)/(1-3*x+x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 07 2019
(GAP) a:=[3, 6, 18];; for n in [4..30] do a[n]:=3*a[n-1]-a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Aug 07 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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