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A125946 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of digits 1,2, at least one of digits 3,4,5 and at least one of digits 6,7,8,9.

%I A125946 #15 Dec 22 2024 20:37:23
%S A125946 10,98,940,8798,80140,709238,6096100,50950718,415060060,3305238278,
%T A125946 25807024660,198131841038,1499550640780,11213044626518,82997777543620,
%U A125946 609099122145758,4437879770746300,32138240678881958,231547934781860980,1661033550903240878
%N A125946 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of digits 1,2, at least one of digits 3,4,5 and at least one of digits 6,7,8,9.
%H A125946 Colin Barker, <a href="/A125946/b125946.txt">Table of n, a(n) for n = 1..1000</a>
%H A125946 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125946 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F A125946 a(n) = 24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1.
%F A125946 G.f.: -2*x*(2520*x^6 -6042*x^5 +6043*x^4 -2783*x^3 +708*x^2 -91*x +5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - _Colin Barker_, Feb 23 2015
%p A125946 f:=n->24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1;
%t A125946 Table[24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1,{n, 20}]  (* _James C. McMahon_, Dec 22 2024 *)
%o A125946 (PARI) vector(100, n, 24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1) \\ _Colin Barker_, Feb 23 2015
%Y A125946 Cf. A125630.
%K A125946 nonn,base,easy
%O A125946 1,1
%A A125946 Aleksandar M. Janjic and _Milan Janjic_, Feb 04 2007