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A125904 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 the digits 1,2,3,4 and at least one of the digits 5,6,7,8,9.

%I A125904 #20 Nov 22 2022 07:10:38
%S A125904 10,100,1000,9976,98920,971440,9420400,90005176,846101080,7822770880,
%T A125904 71163913600,637585923976,5633160763240,49148451899920,
%U A125904 424055315011600,3623013325068376,30689130457473400,258015134469182560,2155143129458730400
%N A125904 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 the digits 1,2,3,4 and at least one of the digits 5,6,7,8,9.
%H A125904 Colin Barker, <a href="/A125904/b125904.txt">Table of n, a(n) for n = 1..1000</a>
%H A125904 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125904 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).
%F A125904 a(n) = 20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1.
%F A125904 G.f.: -2*x*(20160*x^7 -54792*x^6 +53362*x^5 -28337*x^4 +8392*x^3 -1430*x^2 +130*x -5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - _Colin Barker_, Feb 23 2015
%p A125904 f:=n->20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1;
%o A125904 (PARI) vector(100, n, 20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1) \\ _Colin Barker_, Feb 23 2015
%Y A125904 Cf. A125630.
%K A125904 nonn,base,easy
%O A125904 1,1
%A A125904 Aleksandar M. Janjic and _Milan Janjic_, Feb 03 2007