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A125897 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 and at least one of the digits 4,5,6,7,8,9.

%I A125897 #15 Dec 22 2024 21:33:02
%S A125897 10,100,994,9796,95650,924820,8845714,83575396,778945090,7156197940,
%T A125897 64800104434,578648865796,5100362368930,44424892053460,
%U A125897 382839350691154,3268062540952996,27665402010407170,232490197792427380,1941315874498269874
%N A125897 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 and at least one of the digits 4,5,6,7,8,9.
%H A125897 Colin Barker, <a href="/A125897/b125897.txt">Table of n, a(n) for n = 1..1000</a>
%H A125897 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125897 <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 A125897 a(n) = 18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1.
%F A125897 G.f.: -2*x*(20160*x^7 -54792*x^6 +53344*x^5 -28304*x^4 +8374*x^3 -1427*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 A125897 f:=n->18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1;
%t A125897 Table[18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1, {n, 19}]  (* _James C. McMahon_, Dec 22 2024 *)
%o A125897 (PARI) vector(100, n, 18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1) \\ _Colin Barker_, Feb 23 2015
%Y A125897 Cf. A125630.
%K A125897 nonn,base,easy
%O A125897 1,1
%A A125897 Aleksandar M. Janjic and _Milan Janjic_, Feb 03 2007