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a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks digits 1,2,3 and at least one of digits 4,5,6,7,8,9.
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%I #12 Aug 02 2017 11:30:09

%S 7,49,343,2401,16807,116929,803383,5432161,36120007,236404609,

%T 1525601623,9726181921,61371928807,383929313089,2384606035063,

%U 14723095123681,90457525939207,553507860826369,3375536272503703,20528377102849441,124556950506727207

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

%H Colin Barker, <a href="/A126627/b126627.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).

%F a(n) = 6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1.

%F G.f.: -x*(720*x^5 -1764*x^4 +1372*x^3 -539*x^2 +98*x -7) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - _Colin Barker_, Feb 23 2015

%p f:=n->6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1;

%t LinearRecurrence[{21,-175,735,-1624,1764,-720},{7,49,343,2401,16807,116929},30] (* _Harvey P. Dale_, Aug 02 2017 *)

%o (PARI) vector(100, n, 6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1) \\ _Colin Barker_, Feb 23 2015

%Y Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.

%K nonn,base,easy

%O 1,1

%A Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007