|
%I #11 Feb 22 2020 20:35:19
%S 45,855,12600,166500,2070000,24750000,288000000,3285000000,
%T 36900000000,409500000000,4500000000000,49050000000000,
%U 531000000000000,5715000000000000,61200000000000000,652500000000000000,6930000000000000000,73350000000000000000
%N Sum of the digits of all n-digit numbers.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F First differences of A034967: a(n) = 45*n*10^(n-1) - 45*(n-1)10^(n-2) = 45*(9*n+1)*10^(n-2) - _Alexander Adamchuk_, Jan 02 2004
%F G.f.: 45*x*(1 - x)/(1 - 10*x)^2. - _Arkadiusz Wesolowski_, Jul 12 2012
%e The sum of the digits of the two-digit numbers 10, 11, 12, ..., 99 is 855. Therefore a(2) = 855.
%t f[n_] := Module[{i, s}, s = 0; For[i = 10^(n - 1), i < 10^n, i++, s = s + Apply[Plus, IntegerDigits[i]]]; s]; t = Table[f[n], {n, 1, 6}]
%t n=Range[15] a=45*(9*n+1)*10^(n-2) (Adamchuk)
%t Rest[CoefficientList[Series[45x (1-x)/(1-10x)^2,{x,0,20}],x]] (* _Harvey P. Dale_, Aug 26 2019 *)
%Y Cf. A034967.
%K base,nonn
%O 1,1
%A _Joseph L. Pe_, Jan 08 2003
|
