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%I A069183 #15 Sep 22 2025 16:00:38
%S A069183 1,1,3,4,7,9,15,18,27,33,45,54,72,84,108,126,156,180,220,250,300,340,
%T A069183 400,450,525,585,675,750,855,945,1071,1176,1323,1449,1617,1764,1960,
%U A069183 2128,2352,2548,2800,3024,3312,3564,3888,4176,4536,4860,5265,5625,6075
%N A069183 Expansion of 1/((1-x)(1-x^2)^2(1-x^3)(1-x^6)).
%H A069183 G. C. Greubel, <a href="/A069183/b069183.txt">Table of n, a(n) for n = 0..1000</a>
%H A069183 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,3,0,-3,1,2,1,-2,-1,1).
%F A069183 G.f.: 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)).
%F A069183 a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 3*a(n-6) - 3*a(n-8) + a(n-9) + 2*a(n-10) + a(n-11) - 2*a(n-12) - a(n-13) + a(n-14). - _Wesley Ivan Hurt_, May 24 2024
%t A069183 CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^2)^2), {x, 0, 100}], x] (* _Jinyuan Wang_, Mar 15 2020 *)
%o A069183 (PARI) a(n) = polcoeff(1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)+x*O(x^n)), n);
%o A069183 (Magma)
%o A069183 R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)) )); // _G. C. Greubel_, May 26 2024
%o A069183 (SageMath)
%o A069183 def A069183_list(prec):
%o A069183     P.<x> = PowerSeriesRing(ZZ, prec)
%o A069183     return P( 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)) ).list()
%o A069183 A069183_list(60) # _G. C. Greubel_, May 26 2024
%Y A069183 Cf. A029000.
%K A069183 nonn,easy
%O A069183 0,3
%A A069183 _Rick L. Shepherd_, Apr 10 2002

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