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A126632
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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 4,5,6 and at least one of digits 7,8,9.
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3
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9, 79, 669, 5431, 42189, 314119, 2251629, 15625591, 105563469, 697683559, 4529641389, 28986744151, 183339095949, 1148652643399, 7141191155949, 44118519949111, 271168742599629, 1659705919705639, 10123331198091309, 61571999920648471
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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) = 18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1.
G.f.: -x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Feb 22 2015
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EXAMPLE
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a(8) = 15625591.
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MAPLE
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f:=n->18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1;
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PROG
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(PARI) Vec(-x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*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
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CROSSREFS
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Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.
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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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