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A125947 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3,4,5 and at least one of digits 6,7,8,9.

%I A125947 #16 Dec 23 2024 10:43:27
%S A125947 9,81,729,6513,57369,495921,4194969,34689393,280607769,2224214961,
%T A125947 17313344409,132651929073,1002605145369,7490229758001,55407572177049,
%U A125947 406450276733553,2960529995462169,21435301615525041,154414691892116889,1107604165960750833
%N A125947 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3,4,5 and at least one of digits 6,7,8,9.
%H A125947 Colin Barker, <a href="/A125947/b125947.txt">Table of n, a(n) for n = 1..1000</a>
%H A125947 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125947 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F A125947 a(n) = 16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1.
%F A125947 G.f.: -3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - _Colin Barker_, Feb 22 2015
%e A125947 a(8) = 34689393.
%p A125947 f:=n->16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1;
%t A125947 Table[ 16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1, {n, 20}] (* _James C. McMahon_, Dec 23 2024 *)
%o A125947 (PARI) Vec(-3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%Y A125947 Cf. A125630.
%K A125947 nonn,base,easy
%O A125947 1,1
%A A125947 Aleksandar M. Janjic and _Milan Janjic_, Feb 04 2007