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A052268 First differences of 10^n (A011557).

%I A052268 #72 Apr 15 2025 12:05:35
%S A052268 9,90,900,9000,90000,900000,9000000,90000000,900000000,9000000000,
%T A052268 90000000000,900000000000,9000000000000,90000000000000,
%U A052268 900000000000000,9000000000000000,90000000000000000,900000000000000000,9000000000000000000,90000000000000000000
%N A052268 First differences of 10^n (A011557).
%C A052268 a(n) is equal to the number of functions f:{1,2...,n}->{1,2,...,10} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,...,10} we have f(x)<>y. - Aleksandar M. Janjic and _Milan Janjic_, Mar 27 2007
%C A052268 a(n) is the number of n-digit positive integers. - _Geoffrey Critzer_, Apr 23 2009
%D A052268 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D A052268 Miklos Bona, Introduction to Enumerative Combinatorics, McGraw-Hill, 2007, p. 8.
%H A052268 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A052268 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%F A052268 a(n) = 9*10^(n-1).
%F A052268 From _Stefano Spezia_, Jun 03 2021: (Start)
%F A052268 O.g.f.: 9*x/(1 - 10*x).
%F A052268 E.g.f.: 9*(exp(10*x) - 1)/10.
%F A052268 a(n) = 10*a(n-1) for n > 1. (End)
%t A052268 q = 10; Join[{a = 1}, Table[If[n == 0, a = q * a - 1, a = q * a], {n, 0, 25}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t A052268 Differences[10^Range[0, 19]] (* _Alonso del Arte_, Feb 23 2015 *)
%o A052268 (PARI) a(n)=9*10^(n-1) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A052268 Cf. A011557.
%K A052268 easy,nonn
%O A052268 1,1
%A A052268 _Barry E. Williams_, Feb 03 2000
%E A052268 Deleted erroneous term a(0)=1. - _N. J. A. Sloane_, Apr 02 2015