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A143471
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Expansion of 1/(x^10*p(x + 1/x)), where p(x) = 1 - x^3 - x^5 - x^7 + x^10 is a Salem polynomial.
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3
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1, 0, -10, 1, 55, -12, -219, 77, 701, -351, -1900, 1277, 4494, -3966, -9485, 11058, 18342, -29012, -34057, 75053, 65836, -198845, -144194, 547462, 359314, -1548522, -937883, 4396415, 2346732, -12282817, -5272447, 33415657, 9836296, -88340069, -11914604
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,-10,1,-45,8,-120,27,-210,48,-253,48,-210,27,-120,8,-45,1,-10,0,-1).
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FORMULA
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G.f.: 1/(1 + 10*x^2 - x^3 + 45*x^4 - 8*x^5 + 120*x^6 - 27*x^7 + 210*x^8 - 48*x^9 + 253*x^10 - 48*x^11 + 210*x^12 - 27*x^13 + 120*x^14 - 8*x^15 + 45*x^16 - x^17 + 10*x^18 + x^20).
a(n) = -10*a(n-2) + a(n-3) - 45*a(n-4) + 8*a(n-5) - 120*a(n-6) + 27*a(n-7) - 210*a(n-8) + 48*a(n-9) - 253*a(n-10) + 48*a(n-11) - 210*a(n-12) + 27*a(n-13) - 120*a(n-14) + 8*a(n-15) - 45*a(n-16) + a(n-17) - 10*a(n-18) - a(n-20). - Franck Maminirina Ramaharo, Oct 30 2018
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MATHEMATICA
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f[x_] = x^10 - x^7 - x^5 - x^3 + 1;
CoefficientList[Series[1/(x^10*f[x + 1/x]), {x, 0, 40}], x]
LinearRecurrence[{0, -10, 1, -45, 8, -120, 27, -210, 48, -253, 48, -210, 27, -120, 8, -45, 1, -10, 0, -1}, {1, 0, -10, 1, 55, -12, -219, 77, 701, -351, -1900, 1277, 4494, -3966, -9485, 11058, 18342, -29012, -34057, 75053}, 40] (* Harvey P. Dale, Dec 20 2023 *)
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PROG
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(PARI) x='x+O('x^50); Vec(1/(1+10*x^2-x^3+45*x^4-8*x^5+120*x^6-27*x^7 + 210*x^8-48*x^9+253*x^10-48*x^11+210*x^12-27*x^13+120*x^14 - 8*x^15 + 45*x^16-x^17+10*x^18+x^20)) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 + 10*x^2-x^3+45*x^4-8*x^5+120*x^6-27*x^7+210*x^8-48*x^9+253*x^10 - 48*x^11+210*x^12-27*x^13+120*x^14-8*x^15+45*x^16-x^17+10*x^18+x^20))); // G. C. Greubel, Nov 03 2018
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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