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%I #13 Sep 08 2022 08:45:00
%S 0,2,12,58,256,1072,4336,17112,66304,253280,956608,3579680,13292544,
%T 49039360,179912448,656874368,2388205568,8650598912,31231020032,
%U 112419973632,403596148736,1445463642112,5165581660160,18423238924288
%N Row sums of array T as in A054144.
%H G. C. Greubel, <a href="/A054145/b054145.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
%F G.f.: 2*x*(1 - x)^2/(1 - 4*x + 2*x^2)^2.
%F a(n) = ((n-2)*((2 + sqrt(2))^n + (2 - sqrt(2))^n) + sqrt(2)*((2 + sqrt(2))^n - (2 - sqrt(2))^n))/8. - _G. C. Greubel_, Jul 31 2019
%t LinearRecurrence[{8,-20,16,-4}, {0,2,12,58}, 30] (* _G. C. Greubel_, Jul 31 2019 *)
%o (PARI) my(x='x+O('x^30)); concat([0], Vec(2*x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ _G. C. Greubel_, Jul 31 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 2*x*(1-x)^2/(1-4*x+2*x^2)^2 )); // _G. C. Greubel_, Jul 31 2019
%o (Sage) (2*x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 31 2019
%o (GAP) a:=[0,2,12,58];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # _G. C. Greubel_, Jul 31 2019
%K nonn
%O 0,2
%A _Clark Kimberling_, Mar 18 2000