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A125880 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 and at least one of the digits 3,4,5,6,7,8,9.

%I A125880 #13 Dec 22 2024 21:32:26
%S A125880 10,98,946,9026,85330,800738,7463746,69054146,633214450,5746812578,
%T A125880 51574432546,457575310466,4014480866770,34850492651618,
%U A125880 299615359353346,2553264555537986,21587837904314290,181256003521421858,1512536914179602146,12553861394003656706
%N A125880 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 and at least one of the digits 3,4,5,6,7,8,9.
%H A125880 Colin Barker, <a href="/A125880/b125880.txt">Table of n, a(n) for n = 1..1000</a>
%H A125880 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125880 <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 A125880 a(n) = 14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1.
%F A125880 G.f.: -2*x*(20160*x^7 -54792*x^6 +53420*x^5 -28436*x^4 +8441*x^3 -1439*x^2 +131*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 A125880 f:=n->14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1;
%t A125880 Table[14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1,{n,20}] (* _James C. McMahon_, Dec 22 2024 *)
%o A125880 (PARI) vector(100, n, 14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1) \\ _Colin Barker_, Feb 23 2015
%Y A125880 Cf. A125630.
%K A125880 nonn,base,easy
%O A125880 1,1
%A A125880 Aleksandar M. Janjic and _Milan Janjic_, Feb 03 2007, Feb 13 2007