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A205579
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a(n) = round(r^n) where r is the smallest Pisot number (real root r=1.3247179.. of x^3-x-1).
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2
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1, 1, 2, 2, 3, 4, 5, 7, 9, 13, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 43721, 57918, 76725, 101639, 134643, 178364, 236282, 313007, 414646
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein: Pisot Number.
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FORMULA
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G.f.: (1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3).
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MATHEMATICA
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CoefficientList[Series[(1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 19 2012 *)
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PROG
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(PARI)
default(realprecision, 110);
default(format, "g.15");
r=real(polroots(x^3-x-1)[1])
v=vector(66, n, round(r^(n-1)) )
(PARI)
x='x+O('x^66) /* that many terms */
v=Vec((1+x+x^2+x^9+x^10-x^12)/(1-x^2-x^3))
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CROSSREFS
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Cf. A112639 (definition using floor() instead of round()).
Cf. A060006 (decimal expansion of r=1.32471795724475...).
Cf. A051016, A051017.
Sequence in context: A064324 A173090 A032277 * A089047 A133498 A097600
Adjacent sequences: A205576 A205577 A205578 * A205580 A205581 A205582
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt, Jan 29 2012
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STATUS
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approved
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