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A126640 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.

%I A126640 #14 Dec 26 2024 20:30:26
%S A126640 8,60,422,2784,17318,102600,584942,3237504,17516438,93136440,
%T A126640 488625662,2537103024,13068059558,66890498280,340713533582,
%U A126640 1728792901344,8745409322678,44134458900120,222306845468702,1118087142184464,5616691514201798,28188613237893960
%N A126640 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.
%H A126640 Colin Barker, <a href="/A126640/b126640.txt">Table of n, a(n) for n = 1..1000</a>
%H A126640 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A126640 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F A126640 a(n) = 12*5^n-24*4^n+19*3^n-7*2^n+1.
%F A126640 G.f.: -2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Feb 22 2015
%p A126640 f:=n->12*5^n-24*4^n+19*3^n-7*2^n+1;
%t A126640 LinearRecurrence[{15,-85,225,-274,120},{8, 60, 422, 2784, 17318},22] (* _James C. McMahon_, Dec 26 2024 *)
%o A126640 (PARI) Vec(-2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%Y A126640 Cf. A125630, A125948, A125947, A125946, A125945, A125940, A125909, A125908, A125880, A125897, A125904, A125858.
%K A126640 nonn,base,easy
%O A126640 1,1
%A A126640 Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007