cp's OEIS Frontend

A099676 Partial sums of repdigits of A002283.

%I A099676 #41 Sep 13 2023 15:10:28
%S A099676 9,108,1107,11106,111105,1111104,11111103,111111102,1111111101,
%T A099676 11111111100,111111111099,1111111111098,11111111111097,
%U A099676 111111111111096,1111111111111095,11111111111111094,111111111111111093,1111111111111111092,11111111111111111091
%N A099676 Partial sums of repdigits of A002283.
%C A099676 a(n) is the maximal positive integer k such that the sequence 1, 2, 3, 4, ..., k-1, k has a total of n*k digits. - _Bui Quang Tuan_, Mar 12 2015
%H A099676 Vincenzo Librandi, <a href="/A099676/b099676.txt">Table of n, a(n) for n = 1..1000</a>
%H A099676 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).
%F A099676 a(n) = (10/9)*(10^n-1) - n. - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004
%F A099676 From _Colin Barker_, Mar 12 2014: (Start)
%F A099676 a(n) = 12*a(n-1)-21*a(n-2)+10*a(n-3).
%F A099676 G.f.: -9*x / ((x-1)^2*(10*x-1)). (End)
%F A099676 E.g.f.: exp(x)*(10*(exp(9*x) - 1) - 9*x)/9. - _Stefano Spezia_, Sep 13 2023
%e A099676 9 + 99 + 999 + 9999 + 99999 = a(5) = 111105.
%p A099676 a:=n->sum((10^(n-j)-1^(n-j)), j=0..n): seq(a(n), n=1..17); # _Zerinvary Lajos_, Jan 15 2007
%t A099676 <<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
%t A099676 CoefficientList[Series[-9/((x - 1)^2 (10 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 14 2014 *)
%t A099676 LinearRecurrence[{12,-21,10},{9,108,1107},20] (* _Harvey P. Dale_, Apr 18 2015 *)
%o A099676 (Sage) [gaussian_binomial(n,1,10)-n for n in range(2,19)] # _Zerinvary Lajos_, May 29 2009
%o A099676 (PARI) Vec(-9*x/((x-1)^2*(10*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 12 2014
%o A099676 (Magma) [(10/9)*(10^n-1)-n: n in [1..20]]; // _Vincenzo Librandi_, Mar 14 2014
%Y A099676 Cf. A057932, A002275-A002283, A099669-A099674.
%K A099676 base,nonn,easy
%O A099676 1,1
%A A099676 _Labos Elemer_, Nov 17 2004