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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 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.
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%I #18 Oct 14 2016 17:23:12

%S 9,77,633,5021,38409,283277,2019033,13963901,94144809,621444077,

%T 4031587833,25787305181,163054382409,1021372934477,6349128459033,

%U 39222102764861,241061530639209,1475385002210477,8998880800344633,54732125638998941

%N 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 Colin Barker, <a href="/A126631/b126631.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) = 16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1.

%F 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 a(8) = 13963901.

%p f:=n->16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1;

%t LinearRecurrence[{21,-175,735,-1624,1764,-720},{9,77,633,5021,38409,283277},30] (* _Harvey P. Dale_, Oct 14 2016 *)

%o (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 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