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A143619
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Sequence from expansion of polynomial (true Salem polynomial): p(x)=1 - x^2 - x^7 - x^12 + x^14.
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0
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1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 8, 9, 12, 13, 17, 19, 24, 28, 34, 41, 49, 59, 71, 86, 103, 124, 149, 179, 215, 259, 311, 375, 450, 542, 651, 784, 942, 1133, 1363, 1638, 1971, 2369, 2851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,10
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COMMENTS
| Low ratio of 1.20262.
Vector matrix Markov giving the same sequence is:
CompanionMatrix[p_, x_] := Module[{cl = CoefficientList[p, x], deg,
m}, cl = Drop[cl/Last[cl], -1]; deg = Length[cl];
If[deg == 1, {-cl}, m = RotateLeft[
IdentityMatrix[deg]]; m[[ -1]] = -cl; Transpose[m]]];
M = Transpose[CompanionMatrix[1 - x^2 - x^7 - x^12 + x^14, x]];
v[0] = Table[a[[n]], {n, 1, 14}];
v[n_] := v[n] = M.v[n - 1];
Table[v[n][[1]], {n, 0, 50}]
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FORMULA
| p(x)=1 - x^2 - x^7 - x^12 + x^14; a(n) = coefficient_expansion(x^14*p(1/x)).
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MATHEMATICA
| f[x_] = 1 - x^2 - x^7 - x^12 + x^14; g[x] = ExpandAll[x^14*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}];
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CROSSREFS
| Sequence in context: A005044 A029142 A054685 * A029141 A058742 A161227
Adjacent sequences: A143616 A143617 A143618 * A143620 A143621 A143622
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 26 2008
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