A393549 a(n) is the number of n-digit numbers in which at least one digit occurs more than once.

0, 9, 252, 4464, 62784, 763920, 8455680, 88367040, 896734080, 8996734080, 90000000000, 900000000000, 9000000000000, 90000000000000, 900000000000000, 9000000000000000, 90000000000000000, 900000000000000000, 9000000000000000000, 90000000000000000000, 900000000000000000000

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

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

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

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

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

Mathematica

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

Crossrefs

Cf. A007318, A052268, A073531, A109303.

Sequence in context: A160501 A075987 A135099 * A073427 A303050 A194790

Adjacent sequences: A393546 A393547 A393548 * A393550 A393551 A393552

Keyword

nonn,base,easy

Author

Stefano Spezia, Mar 20 2026

Status

approved