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%I #13 Jun 13 2015 00:52:17
%S 8,64,512,4096,32768,262144,2092112,16595776,130437728,1013866624,
%T 7788438512,59145432256,444357721088,3306242197504,24389881261712,
%U 178578361769536,1299058046034848,9397253451942784,67653687455953712,485065987257543616
%N a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1 and 2 and at least one of digits 3,4,5,6,7,8,9.
%H Colin Barker, <a href="/A125908/b125908.txt">Table of n, a(n) for n = 1..1000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).
%F a(n) = 7*7^n-21*6^n+35*5^n-35*4^n+21*3^n-7*2^n+1.
%F G.f.: -8*x*(630*x^6 -1476*x^5 +1457*x^4 -664*x^3 +162*x^2 -20*x +1)/((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - _Colin Barker_, Feb 22 2015
%e a(8) = 16595776.
%p f:=n->7*7^n-21*6^n+35*5^n-35*4^n+21*3^n-7*2^n+1;
%o (PARI) Vec(-8*x*(630*x^6-1476*x^5+1457*x^4-664*x^3+162*x^2-20*x+1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%Y Cf. A125630.
%K nonn,base,easy
%O 1,1
%A Aleksandar M. Janjic and _Milan Janjic_, Feb 04 2007
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