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%I A027025 #13 Sep 08 2022 08:44:49
%S A027025 1,11,33,77,161,319,613,1157,2161,4011,7417,13685,25217,46431,85453,
%T A027025 157229,289249,532075,978705,1800189,3311137,6090207,11201717,
%U A027025 20603253,37895377,69700555,128199401,235795557,433695745,797690943
%N A027025 a(n) = T(n,n+3), T given by A027023.
%H A027025 G. C. Greubel, <a href="/A027025/b027025.txt">Table of n, a(n) for n = 3..1002</a>
%H A027025 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,-1,1).
%F A027025 G.f.: x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)).
%F A027025 a(n) = A000213(n+3) -4*(n+1). - _R. J. Mathar_, Jun 24 2020
%p A027025 seq(coeff(series(x^4/((1+2*x)*(2*x^3+x^2-2*x+1)), x, n+1), x, n), n = 3..40); # _G. C. Greubel_, Nov 04 2019
%t A027025 Drop[CoefficientList[Series[x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)), {x,0,40}], x], 3] (* or *) LinearRecurrence[{3,-2,0,-1,1}, {1, 11,33,77,161}, 40] (* _G. C. Greubel_, Nov 04 2019 *)
%o A027025 (PARI) my(x='x+O('x^40)); Vec(x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 04 2019
%o A027025 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 04 2019
%o A027025 (Sage)
%o A027025 def A077952_list(prec):
%o A027025     P.<x> = PowerSeriesRing(ZZ, prec)
%o A027025     return P(x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3))).list()
%o A027025 a=A077952_list(40); a[3:] # _G. C. Greubel_, Nov 04 2019
%o A027025 (GAP) a:=[1,11,33,77,161];; for n in [6..30] do a[n]:=3*a[n-1]-2*a[n-2]-a[n-4] +a[n-5]; od; a; # _G. C. Greubel_, Nov 04 2019
%K A027025 nonn,easy
%O A027025 3,2
%A A027025 _Clark Kimberling_

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