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a(n) = T(n,n+2), T given by A027023.
4

%I #18 Sep 08 2022 08:44:49

%S 1,5,13,27,53,101,189,351,649,1197,2205,4059,7469,13741,25277,46495,

%T 85521,157301,289325,532155,978789,1800277,3311229,6090303,11201817,

%U 20603357,37895485,69700667,128199517,235795677,433695869

%N a(n) = T(n,n+2), T given by A027023.

%H G. C. Greubel, <a href="/A027024/b027024.txt">Table of n, a(n) for n = 2..1001</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).

%F G.f.: x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)).

%F a(n) = a(n-1) + a(n-2) + a(n-3) + 8, for n>4. - _Greg Dresden_, Feb 09 2020

%F a(n) = A000213(n+2)-4. - _R. J. Mathar_, Jun 24 2020

%p seq(coeff(series(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2..35); # _G. C. Greubel_, Nov 04 2019

%t Drop[CoefficientList[Series[x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), {x, 0, 35}], x], 2] (* or *) LinearRecurrence[{2,0,0,-1}, {1,5,13,27}, 35] (* _G. C. Greubel_, Nov 04 2019 *)

%o (PARI) my(x='x+O('x^35)); Vec(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 04 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 04 2019

%o (Sage)

%o def A027024_list(prec):

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

%o return P( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) ).list()

%o a=A027024_list(35); a[2:] # _G. C. Greubel_, Nov 04 2019

%o (GAP) a:=[1,5,13,27];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-4]; od; a; # _G. C. Greubel_, Nov 04 2019

%Y Pairwise sums of A027053.

%K nonn,easy

%O 2,2

%A _Clark Kimberling_