(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // G. C. Greubel, May 12 2019

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a(n) = 8*a(n-1)+8*a(n-2)+8*a(n-3)+8*a(n-4)-36*a(n-5). - Wesley Ivan Hurt, May 10 2021

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G.f. : (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

CoefficientList[Series[(t1+x)*(1-x^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + )/(1)/(-9*x+44*x^5-36*t^5 - 8*t^4 - 8*t^3 - 8*tx^2 - 8*t + 16), {t, x, 0, 5030}], tx] (* or *) Join[{1}, LinearRecurrence[{8, 8, 8, 8, -36}, {1, 10, 90, 810, 7290, 65565}, 50]30] (* G. C. Greubel, Dec 21 2016 *)

coxG[{5, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

(PARI) Vec((t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1) + O(t^50)) \\ G. C. Greubel, Dec 21 2016 *)

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)) \\ G. C. Greubel, Dec 21 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // G. C. Greubel, May 12 2019

(Sage) ((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

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G. C. Greubel, <a href="/A163397/b163397.txt">Table of n, a(n) for n = 0..1000</a>

G.f. (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

8*t + 1)

CoefficientList[Series[(t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1), {t, 0, 50}], t] (* or *) Join[{1}, LinearRecurrence[{8, 8, 8, 8, -36}, {10, 90, 810, 7290, 65565}, 50]] (* G. C. Greubel, Dec 21 2016 *)

(PARI) Vec((t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1) + O(t^50)) \\ G. C. Greubel, Dec 21 2016 *)

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