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%I #20 Sep 08 2022 08:45:50
%S 5,9,49,449,4449,44449,444449,4444449,44444449,444444449,4444444449,
%T 44444444449,444444444449,4444444444449,44444444444449,
%U 444444444444449,4444444444444449,44444444444444449,444444444444444449
%N a(n) = (4*10^n + 41)/9.
%H Vincenzo Librandi, <a href="/A173776/b173776.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F a(n) = 10*a(n-1) - 41 with n>0, a(0)=5.
%F G.f.: (5 - 46*x)/((1-x)*(1-10*x)). - _Vincenzo Librandi_, Jul 05 2012
%F a(n) = 11*a(n-1) -10*a(n-2). - _Vincenzo Librandi_, Jul 05 2012
%F E.g.f.: (1/9)*(41*exp(x) + 4*exp(10*x)). - _G. C. Greubel_, Jul 06 2021
%t Join[{5}, FromDigits/@Table[PadLeft[{9}, n, 4], {n,20}]] (* or *) Join[{5}, NestList[10#-41&, 9, 20]] (* _Harvey P. Dale_, Feb 17 2012 *)
%t CoefficientList[Series[(5-46*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 05 2012 *)
%o (Magma) [(4*10^n+41)/9: n in [0..20]]; // _Vincenzo Librandi_, Jul 05 2012
%o (Sage) [(4*10^n + 41)/9 for n in (0..30)] # _G. C. Greubel_, Jul 06 2021
%Y Cf. A093402.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Feb 24 2010
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