A393549 - OEIS

%I #19 Mar 24 2026 23:14:42

%S 0,9,252,4464,62784,763920,8455680,88367040,896734080,8996734080,

%T 90000000000,900000000000,9000000000000,90000000000000,

%U 900000000000000,9000000000000000,90000000000000000,900000000000000000,9000000000000000000,90000000000000000000,900000000000000000000

%N a(n) is the number of n-digit numbers in which at least one digit occurs more than once.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%F a(n) = 9*(10^(n-1) - 9!/(10 - n)!) for n <= 10.

%F a(n) = 9*10^(n-1) for n > 10.

%F a(n) = 10*a(n-1) for n > 11.

%F E.g.f.: 9*(exp(10*x) - (1 + x)^10)/10.

%t a[n_]:=9*(10^(n-1)-9!/(10-n)!); Array[a,21]

%Y Cf. A007318, A052268, A073531, A109303.

%K nonn,base,easy

%O 1,2

%A _Stefano Spezia_, Mar 20 2026