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A143644
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Expansion of 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14) (a Salem polynomial).
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23
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1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 9, 10, 12, 15, 18, 21, 26, 31, 37, 44, 54, 64, 76, 92, 111, 132, 159, 191, 229, 275, 330, 396, 475, 570, 684, 821, 985, 1182, 1418, 1703, 2043, 2451, 2942, 3531, 4236, 5084, 6101, 7321, 8785, 10543, 12652, 15182, 18219, 21864, 26237, 31485
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OFFSET
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0,11
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COMMENTS
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Limiting ratio is 1.2000265239873915..., the largest real root of 1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14: 1.200026523987391518902962100414 is a candidate for the smallest degree-14 Salem number. The absolute values of the roots of the polynomial are 0.8333149143..., 1.200026523..., and 1.0 (with multiplicity 12). The polynomial is self-reciprocal. - Joerg Arndt, Nov 03 2012
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,-1,0,0,1,1,0,0,-1).
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FORMULA
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G.f.: 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14). - Colin Barker, Nov 03 2012
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MAPLE
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seq(coeff(series(1/(1-x^3-x^4+x^7-x^10-x^11+x^14), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 06 2019
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MATHEMATICA
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CoefficientList[Series[1/(1-x^3-x^4+x^7-x^10-x^11+x^14), {x, 0, 50}], x]
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PROG
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(PARI) my(x='x+O('x^50)); Vec(1/(1-x^3-x^4+x^7-x^10-x^11+x^14)) \\ G. C. Greubel, Dec 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) )); // G. C. Greubel, Dec 06 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) ).list()
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CROSSREFS
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Cf. A029826, A117791, A143419, A143438, A143472, A143619, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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