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A192937 a(n) = 100*a(n-1) - (n-1) with a(1)=100.

%I A192937 #31 Sep 08 2022 08:45:58
%S A192937 100,9999,999898,99989797,9998979696,999897969595,99989796959494,
%T A192937 9998979695949393,999897969594939292,99989796959493929191,
%U A192937 9998979695949392919090,999897969594939291908989
%N A192937 a(n) = 100*a(n-1) - (n-1) with a(1)=100.
%H A192937 Vincenzo Librandi, <a href="/A192937/b192937.txt">Table of n, a(n) for n = 1..300</a>
%H A192937 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (102,-201,100).
%F A192937 From _Bruno Berselli_, Aug 02 2011: (Start)
%F A192937 G.f.: x*(100-201*x+100*x^2)/((1-100*x)*(1-x)^2).
%F A192937 a(n) = (9800*100^n+99*n+1)/9801. (End)
%e A192937 For n=2: a(2)=100*a(1)-(2-1)=100*100-1=10000-1=9999.
%e A192937 For n=3: a(3)=100*a(2)-(3-1)=100*9999-2=999900-2=999898.
%p A192937 a[1]:=100; for n from 2 to 12 do a[n]:=100*a[n-1]-(n-1); end do;
%t A192937 LinearRecurrence[{102,-201,100}, {100,9999,999898}, 20] (* _G. C. Greubel_, Feb 06 2019 *)
%t A192937 RecurrenceTable[{a[1]==100,a[n]==100a[n-1]-n+1},a,{n,20}] (* _Harvey P. Dale_, May 17 2019 *)
%o A192937 (Magma) [n lt 2 select 100 else 100*Self(n-1)-n+1: n in [1..14]];  // _Bruno Berselli_, Aug 02 2011
%o A192937 (PARI) vector(20, n, (98*10^(2*n+2) +99*n +1)/9801) \\ _G. C. Greubel_, Feb 06 2019
%o A192937 (Sage) [(98*10^(2*n+2) +99*n +1)/9801 for n in (1..20)] # _G. C. Greubel_, Feb 06 2019
%o A192937 (GAP) List([1..20], n -> (98*10^(2*n+2) +99*n +1)/9801); # _G. C. Greubel_, Feb 06 2019
%K A192937 nonn,easy
%O A192937 1,1
%A A192937 _Francesco Daddi_, Aug 02 2011