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A359271 Number of odd digits necessary to write all nonnegative n-digit integers.

%I A359271 #31 Dec 29 2022 06:47:55
%S A359271 5,95,1400,18500,230000,2750000,32000000,365000000,4100000000,
%T A359271 45500000000,500000000000,5450000000000,59000000000000,
%U A359271 635000000000000,6800000000000000,72500000000000000,770000000000000000,8150000000000000000
%N A359271 Number of odd digits necessary to write all nonnegative n-digit integers.
%H A359271 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F A359271 a(n) = 5 * (9*n+1) * 10^(n-2).
%F A359271 a(n) = A279766(10^n-1) - A279766(10^(n-1)-1).
%F A359271 a(n) = A113119(n) - A358439(n).
%F A359271 From _Stefano Spezia_, Dec 24 2022: (Start)
%F A359271 O.g.f.: 5*x*(1 - x)/(1 - 10*x)^2.
%F A359271 E.g.f.: (exp(10*x)*(1 + 90*x) - 1)/20. (End)
%e A359271 To write the integers from 10 up to 99, each of the digits 1, 3, 5, 7 and 9, must be used 19 times, hence a(2) = 19*5 = 95.
%p A359271 seq(5 * (9*n+1) * 10^(n-2), n=1..18);
%t A359271 a[n_] := 5*(9*n + 1)*10^(n - 2); Array[a, 20] (* _Amiram Eldar_, Dec 23 2022 *)
%Y A359271 Cf. A113119, A196564, A279766, A358439.
%K A359271 nonn,base,easy
%O A359271 1,1
%A A359271 _Bernard Schott_, Dec 23 2022