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A125948 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 1,2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.

%I A125948 #16 Dec 23 2024 10:43:11
%S A125948 10,100,982,9388,86950,778780,6748822,56713708,463661830,3700940860,
%T A125948 28941318262,222422713228,1684544507110,12602134130140,93308618633302,
%U A125948 684912371803948,4990975002030790,36147245625290620,260449744313893942
%N A125948 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 1,2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.
%H A125948 Colin Barker, <a href="/A125948/b125948.txt">Table of n, a(n) for n = 1..1000</a>
%H A125948 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125948 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F A125948 a(n) = 27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1.
%F A125948 G.f.: -2*x*(2520*x^6 -6012*x^5 +5990*x^4 -2754*x^3 +701*x^2 -90*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 A125948 f:=n->27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1;
%t A125948 Table[27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1,{n,19}] (* _James C. McMahon_, Dec 23 2024 *)
%o A125948 (PARI) vector(100, n, 27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1) \\ _Colin Barker_, Feb 23 2015
%Y A125948 Cf. A125630.
%K A125948 nonn,base,easy
%O A125948 1,1
%A A125948 Aleksandar M. Janjic and _Milan Janjic_, Feb 04 2007