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A126631 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.

%I A126631 #18 Oct 14 2016 17:23:12
%S A126631 9,77,633,5021,38409,283277,2019033,13963901,94144809,621444077,
%T A126631 4031587833,25787305181,163054382409,1021372934477,6349128459033,
%U A126631 39222102764861,241061530639209,1475385002210477,8998880800344633,54732125638998941
%N A126631 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.
%H A126631 Colin Barker, <a href="/A126631/b126631.txt">Table of n, a(n) for n = 1..1000</a>
%H A126631 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A126631 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).
%F A126631 a(n) = 16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1.
%F A126631 G.f.: -x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - _Colin Barker_, Feb 22 2015
%e A126631 a(8) = 13963901.
%p A126631 f:=n->16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1;
%t A126631 LinearRecurrence[{21,-175,735,-1624,1764,-720},{9,77,633,5021,38409,283277},30] (* _Harvey P. Dale_, Oct 14 2016 *)
%o A126631 (PARI) Vec(-x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*x-9)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%Y A126631 Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.
%K A126631 nonn,base,easy
%O A126631 1,1
%A A126631 Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007