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G.f.: (1+x)*(1-x^1211)/(1 - 18*x + 170*x^11 - 153*x^12). (End)

With[{ap=153, bq=17}, CoefficientList[Series[(1+t)*(1-t^1211)/(1-(bq+1)*t + (ap+bq)*t^11-ap*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)

Coefficients(R!( (1+x)*(1-x^1211)/(1-18*x+170*x^11-153*x^12) )); // G. C. Greubel, Jul 23 2024

return P( (1+x)*(1-x^1211)/(1-18*x+170*x^11-153*x^12) ).list()

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<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

From G. C. Greubel, Jul 23 2024: (Start)

a(n) = 17*Sum_{j=1..10} a(n-j) - 153*a(n-11).

G.f.: (1+x)*(1-x^12)/(1 - 18*x + 170*x^11 - 153*x^12). (End)

CoefficientList[Series[(t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 12 2016 *)

With[{a=153, b=17}, CoefficientList[Series[(1+t)*(1-t^12)/(1-(b+1)*t + (a+b)*t^11-a*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)

(Magma)

R<x>:=PowerSeriesRing(Integers(), 30);

Coefficients(R!( (1+x)*(1-x^12)/(1-18*x+170*x^11-153*x^12) )); // G. C. Greubel, Jul 23 2024

(SageMath)

def A166413_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x)*(1-x^12)/(1-18*x+170*x^11-153*x^12) ).list()

A166413_list(30) # G. C. Greubel, Jul 23 2024

Cf. A154638, A169452, A170738.

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coxG[{11, 153, -17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 26 2022 *)

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<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

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