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%I A053730 #19 Sep 08 2022 08:45:00
%S A053730 1,2,6,20,64,192,544,1472,3840,9728,24064,58368,139264,327680,761856,
%T A053730 1753088,3997696,9043968,20316160,45350912,100663296,222298112,
%U A053730 488636416,1069547520,2332033024,5066719232,10972299264,23689428992
%N A053730 a(n) = 2^(n-2)*(n^2 - n + 4).
%H A053730 Vincenzo Librandi, <a href="/A053730/b053730.txt">Table of n, a(n) for n = 0..1000</a>
%H A053730 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A053730 G.f.: (1-4*x+6*x^2)/(1-2*x)^3. - _Colin Barker_, Apr 01 2012
%F A053730 a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3). - _Vincenzo Librandi_, Apr 28 2012
%F A053730 a(n) = Sum_{k=0..n} binomial(n,k) * A077028(n,k), where A077028(n,k) = (n-k)*k + 1. - _Paul D. Hanna_, Oct 11 2015
%p A053730 seq(2^(n-2)*(n^2 -n +4), n=0..30); # _G. C. Greubel_, Sep 06 2019
%t A053730 CoefficientList[Series[(1-4*x+6*x^2)/(1-2*x)^3,{x,0,30}],x] (* _Vincenzo Librandi_, Apr 28 2012 *)
%t A053730 LinearRecurrence[{6,-12,8}, {1,2,6}, 30] (* _G. C. Greubel_, Sep 06 2019 *)
%o A053730 (Magma) I:=[1, 2, 6]; [n le 3 select I[n] else 6*Self(n-1)-12*Self(n-2) +8*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Apr 28 2012
%o A053730 (PARI) vector(30, n, 2^(n-3)*(n^2 -3*n +6)) \\ _G. C. Greubel_, Sep 06 2019
%o A053730 (Sage) [2^(n-2)*(n^2 -n +4) for n in (0..30)] # _G. C. Greubel_, Sep 06 2019
%o A053730 (GAP) List([0..30], n-> 2^(n-2)*(n^2 -n +4)); # _G. C. Greubel_, Sep 06 2019
%Y A053730 Cf. A053545.
%K A053730 nonn,easy
%O A053730 0,2
%A A053730 _N. J. A. Sloane_, Mar 24 2000

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