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A125947
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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 2,3,4,5 and at least one of digits 6,7,8,9.
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19
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9, 81, 729, 6513, 57369, 495921, 4194969, 34689393, 280607769, 2224214961, 17313344409, 132651929073, 1002605145369, 7490229758001, 55407572177049, 406450276733553, 2960529995462169, 21435301615525041, 154414691892116889, 1107604165960750833
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1.
G.f.: -3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((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
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EXAMPLE
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a(8) = 34689393.
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MAPLE
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f:=n->16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1;
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PROG
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(PARI) Vec(-3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((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
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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