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A064617
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a(n) = (10^n - 1)*(80/81) + n/9.
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9
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9, 98, 987, 9876, 98765, 987654, 9876543, 98765432, 987654321, 9876543210, 98765432099, 987654320988, 9876543209877, 98765432098766, 987654320987655, 9876543209876544, 98765432098765433, 987654320987654322, 9876543209876543211, 98765432098765432100, 987654320987654320989
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OFFSET
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1,1
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COMMENTS
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a(n)/10^n converges to 80/81 = 0.987654320987654320...
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LINKS
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FORMULA
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a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3).
G.f.: x*(10*x - 9)/((x - 1)^2*(10*x - 1)). (End)
E.g.f.: exp(x)*(80*exp(9*x) + 9*x - 80)/81. - Stefano Spezia, May 28 2023
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EXAMPLE
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Curious multiplications:
1*8 + 1 = 9;
12*8 + 2 = 98;
123*8 + 3 = 987;
1234*8 + 4 = 9876;
12345*8 + 5 = 98765;
123456*8 + 6 = 987654;
1234567*8 + 7 = 9876543;
12345678*8 + 8 = 98765432;
123456789*8 + 9 = 987654321.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{12, -21, 10}, {9, 98, 987}, 30] (* Harvey P. Dale, Aug 20 2023 *)
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PROG
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(PARI) { a=0; for (n=1, 150, a=10*a + 10 - n; write("b064617.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 20 2009
(PARI) Vec(x*(10*x-9)/((x-1)^2*(10*x-1)) + O(x^100)) \\ Colin Barker, Sep 15 2014
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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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EXTENSIONS
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STATUS
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approved
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