This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014925 #37 May 29 2025 17:31:32
%S A014925 1,21,321,4321,54321,654321,7654321,87654321,987654321,10987654321,
%T A014925 120987654321,1320987654321,14320987654321,154320987654321,
%U A014925 1654320987654321,17654320987654321,187654320987654321,1987654320987654321,20987654320987654321,220987654320987654321
%N A014925 Number of zeros in numbers 1 to 111...1 (n+1 digits).
%H A014925 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).
%F A014925 a(1) = 1; for n>1, a(n) = n*10^(n-1) + a(n-1).
%F A014925 G.f.: x/((1-x)*(1-10*x)^2).
%F A014925 a(n) = 10^n*(n+1)/9 - (1/81)*10^(n+1) + 1/81.
%F A014925 a(n) = (10^n*(9*n - 1) + 1)/81. - _Kenneth E. Caviness_, Mar 30 2011
%F A014925 E.g.f.: (1 - exp(9*x) + 90*x*exp(9*x))*exp(x)/81. - _Ilya Gutkovskiy_, May 02 2016
%F A014925 a(n) = Sum_{i=0..n} i*10^(i-1). - _José de Jesús Camacho Medina_, Dec 14 2016
%F A014925 From _Elmo R. Oliveira_, May 24 2025: (Start)
%F A014925 a(n) = 20*a(n-1) - 100*a(n-2) + 1 for n > 2.
%F A014925 a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3) for n > 3. (End)
%o A014925 (Magma) [(10^n*(9*n-1)+1)/81: n in [1..25]]; // _Vincenzo Librandi_, Mar 31 2011
%o A014925 (PARI) a(n) = sum(i=0, n, i*10^(i-1)); \\ _Michel Marcus_, Dec 15 2016
%o A014925 (PARI) my(x='x+O('x^21)); Vec(-x/((x-1)*(10*x-1)^2)) \\ _Elmo R. Oliveira_, May 24 2025
%Y A014925 Cf. A033713.
%K A014925 nonn,easy,base
%O A014925 1,2
%A A014925 _Olivier Gérard_
%E A014925 Better description from _Stephen G Penrice_, Oct 03 2000
%E A014925 More terms from _Elmo R. Oliveira_, May 24 2025