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A126635
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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 digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.
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3
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7, 47, 307, 1943, 11827, 69287, 392707, 2166743, 11703187, 62168327, 325983907, 1692105143, 8714154547, 44600020967, 227161443907, 1152585909143, 5830444893907, 29423488811207, 148206112628707, 745396075770743, 3744474953809267, 18792450661083047
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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) = 8*5^n-16*4^n+14*3^n-6*2^n+1.
G.f.: -x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015
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MAPLE
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f:=n->8*5^n-16*4^n+14*3^n-6*2^n+1;
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MATHEMATICA
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LinearRecurrence[{15, -85, 225, -274, 120}, {7, 47, 307, 1943, 11827}, 30] (* Harvey P. Dale, Dec 31 2021 *)
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PROG
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(PARI) Vec(-x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*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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