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A125910
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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 and at least one of digits 5,6,7,8,9.
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11
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9, 81, 723, 6381, 55539, 475461, 3993243, 32857101, 264890019, 2094889941, 16282118763, 124625344221, 941303216499, 7029057066021, 51980086628283, 381227207181741, 2776407821318979, 20100192515299701, 144786930345697803, 1038495372200033661
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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) = 15*7^n-45*6^n+65*5^n-55*4^n+28*3^n-8*2^n+1.
G.f.: -3*x*(1680*x^6 -3976*x^5 +3946*x^4 -1807*x^3 +451*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) = 32857101.
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MAPLE
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f:=n->15*7^n-45*6^n+65*5^n-55*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 -3976*x^5 +3946*x^4 -1807*x^3 +451*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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