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%I #34 Sep 13 2023 11:06:37
%S 1,21,321,4321,54321,654321,7654321,87654321,987654321,10987654321,
%T 120987654321,1320987654321,14320987654321,154320987654321,
%U 1654320987654321,17654320987654321,187654320987654321
%N Number of zeros in numbers 1 to 111...1 (n+1 digits).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).
%F a(1) = 1; for n>1, a(n) = n*10^(n-1)+a(n-1).
%F G.f.: x/((1-x)*(1-10*x)^2).
%F a(n) = 10^n*(n+1)/9-1/81*10^(n+1)+1/81.
%F a(n) = (10^n*(9*n-1)+1)/81. - _Kenneth E. Caviness_, Mar 30 2011
%F E.g.f.: (1 - exp(9*x) + 90*x*exp(9*x))*exp(x)/81. - _Ilya Gutkovskiy_, May 02 2016
%F a(n) = Sum_{i=0..n}(i*10^(i-1)). - _José de Jesús Camacho Medina_, Dec 14 2016
%o (Magma) [(10^n*(9*n-1)+1)/81: n in [1..25]]; // _Vincenzo Librandi_, Mar 31 2011
%o (PARI) a(n) = sum(i=0, n, i*10^(i-1)); \\ _Michel Marcus_, Dec 15 2016
%Y Cf. A033713.
%K nonn,easy,base
%O 1,2
%A _Olivier Gérard_
%E Better description from _Stephen G Penrice_, Oct 03 2000