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%I A032343 #19 May 25 2024 15:53:57
%S A032343 0,1,14,149,1506,15085,150886,1508909,15089154,150891621,1508916310,
%T A032343 15089163221,150891632354,1508916323709,15089163237286,
%U A032343 150891632373085,1508916323731106,15089163237311349,150891632373113814
%N A032343 a(n) = 10*a(n-1)+n^2, a(0)=0.
%C A032343 a(n)/10^n converges to 110/729=0.15089163237311...
%H A032343 Vincenzo Librandi, <a href="/A032343/b032343.txt">Table of n, a(n) for n = 0..1000</a>
%H A032343 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,-33,31,-10).
%F A032343 a(n) =(10^n-1)*(110/729)-n^2/9-n*(20/81).
%F A032343 G.f.: (x^2+x)/((x-1)^3*(10*x-1)). - _Harvey P. Dale_, Mar 20 2011
%t A032343 CoefficientList[Series[(x^2+x)/((x-1)^3 (10x-1)),{x,0,30}],x]  (* _Harvey P. Dale_, Mar 20 2011 *)
%t A032343 RecurrenceTable[{a[0] == 0, a[n] == 10*a[n-1] + n^2}, a, {n, 100}] (* _Vincenzo Librandi_, Mar 10 2013 *)
%t A032343 LinearRecurrence[{13,-33,31,-10},{0,1,14,149},20] (* _Harvey P. Dale_, May 25 2024 *)
%o A032343 (Magma) [0] cat [n le 1 select n else 10*Self(n-1)+n^2: n in [1..20]]; // _Vincenzo Librandi_, Mar 10 2013
%Y A032343 Cf. A014824, A019521.
%K A032343 nonn,easy
%O A032343 0,3
%A A032343 _Henry Bottomley_, Jul 04 2000

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