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%I #21 Oct 03 2023 14:07:54
%S 1,2,21,301,4001,50001,600001,7000001,80000001,900000001,10000000001,
%T 110000000001,1200000000001,13000000000001,140000000000001,
%U 1500000000000001,16000000000000001,170000000000000001,1800000000000000001,19000000000000000001
%N Number of times 1 is used in writing out all numbers 1 through 10^n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).
%F a(n) = n*10^(n-1) + 1.
%F a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - _Colin Barker_, May 23 2014
%F G.f.: -(99*x^2-19*x+1) / ((x-1)*(10*x-1)^2). - _Colin Barker_, May 23 2014
%F a(n) = A094798(A011557(n)). - _Michel Marcus_, Oct 03 2023
%t Table[ n*10^(n - 1) + 1, {n, 0, 17}] (* _Robert G. Wilson v_, Jun 15 2004 *)
%t LinearRecurrence[{21,-120,100},{1,2,21},20] (* _Harvey P. Dale_, Sep 07 2022 *)
%o (PARI) Vec(-(99*x^2-19*x+1)/((x-1)*(10*x-1)^2) + O(x^100)) \\ _Colin Barker_, May 23 2014
%Y Cf. A072290, A078427.
%Y Cf. A011557, A094798.
%K base,nonn,easy
%O 0,2
%A _Lekraj Beedassy_, Jun 11 2004
%E More terms from _Robert G. Wilson v_, Jun 15 2004
%E Further terms from _Colin Barker_, May 23 2014
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