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%I #20 Mar 12 2024 14:50:27
%S 1,3,7,14,28,57,115,230,460,921,1843,3686,7372,14745,29491,58982,
%T 117964,235929,471859,943718,1887436,3774873,7549747,15099494,
%U 30198988,60397977,120795955,241591910,483183820,966367641,1932735283,3865470566,7730941132,15461882265
%N Number of n-digit numbers that are divisible by 5^n.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-2).
%F Limit_{n -> oo} a(n+1)/a(n) = 2.
%F a(n) = [(9/10)*2^n]. - _David W. Wilson_, Jun 18 2009
%F G.f.: x * ( 1+x^2-x^3 ) / ( (x-1)*(2*x-1)*(x^2+1) ). - _R. J. Mathar_, Feb 20 2011
%e a(1)=1 because 5 divides only 5,
%e a(2)=3 because 25 divides {25, 50 & 75},
%e a(3)=7 because 125 divides {125, 250, 375, 500, 625, 750 & 925}, etc.
%t f[n_] := Floor[(10^n - 1)/5^n] - Floor[10^(n - 1)/5^n]; Array[f, 35]
%t LinearRecurrence[{3,-3,3,-2},{1,3,7,14},30] (* _Harvey P. Dale_, Feb 20 2016 *)
%Y Cf. A151752.
%K nonn,base,easy
%O 1,2
%A _Robert G. Wilson v_, Jun 17 2009
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