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A081552 Leading terms of rows in A081551.

%I A081552 #27 Jun 30 2025 14:17:07
%S A081552 1,11,102,1003,10004,100005,1000006,10000007,100000008,1000000009,
%T A081552 10000000010,100000000011,1000000000012,10000000000013,
%U A081552 100000000000014,1000000000000015,10000000000000016,100000000000000017,1000000000000000018
%N A081552 Leading terms of rows in A081551.
%C A081552 More generally, a(n) = B^K + n; K = floor(log_B a(n-1)) + 1. This sequence has B=10, a(0)=1; A006127 has B=2, a(0)=1; A052944 has B=2, a(0)=2; A104743 has B=3, a(0)=1; A104745 has B=5, a(0)=1. - _Ctibor O. Zizka_, Mar 22 2008
%H A081552 Vincenzo Librandi, <a href="/A081552/b081552.txt">Table of n, a(n) for n = 1..300</a>
%H A081552 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).
%F A081552 a(n) = 10^(n-1) + n-1.
%F A081552 G.f.: x*(1 -x -9*x^2)/((1-10*x)*(1-x)^2). - _Vincenzo Librandi_, Jun 16 2013
%F A081552 a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). - _Vincenzo Librandi_, Jun 16 2013
%F A081552 E.g.f.: (1/10)*(9 - 10*(1-x)*exp(x) + exp(10*x)). - _G. C. Greubel_, May 27 2021
%p A081552 seq(10^(n-1) +n-1, n=1..40); # _G. C. Greubel_, May 27 2021
%t A081552 Table[10^(n-1) +n-1, {n,30}] (* or *) CoefficientList[Series[(1-x-9x^2)/((1-10x)(1-x)^2), {x, 0, 30}], x]  (* _Vincenzo Librandi_, Jun 16 2013 *)
%o A081552 (Magma) [10^(n-1)+n-1: n in [1..20]]; // _Vincenzo Librandi_, Jun 16 2013
%o A081552 (Magma) I:=[1, 11, 102]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 16 2013
%o A081552 (Sage) [10^(n-1) +n-1 for n in (1..40)] # _G. C. Greubel_, May 27 2021
%Y A081552 Cf. A011557, A081551, A081553, A085952 (first differences, after n=2).
%K A081552 base,easy,nonn
%O A081552 1,2
%A A081552 _Amarnath Murthy_, Apr 01 2003