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A083446
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a(n) = ((10^n - 1) - 9^n)/9.
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2
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2, 30, 382, 4550, 52062, 579670, 6328142, 68064390, 723690622, 7624326710, 79730051502, 828681574630, 8569245282782, 88234318656150, 905219979016462, 9258090922259270, 94433929411444542, 961016475814111990
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OFFSET
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2,1
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COMMENTS
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Let k(n) be the largest n-digit number, 10^n - 1, and let m(n) be the product of its digits, 9^n; then a(n) = (k(n) - m(n))/9.
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LINKS
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FORMULA
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G.f.: 2*x^2*(1-5*x)/((1-x)*(1-9*x)*(1-10*x)).
a(n) = 20*a(n-1) - 109*a(n-2) + 90*a(n-3). - Matthew House, Jan 16 2017
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EXAMPLE
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a(4) = (9999 - 9*9*9*9)/9 = 382.
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MATHEMATICA
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LinearRecurrence[{20, -109, 90}, {2, 30, 382}, 20] (* Harvey P. Dale, Oct 12 2017 *)
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PROG
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(PARI) for (i=2, 30, print1(((10^n -1) - 9^n)/9, ", "))))
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003
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EXTENSIONS
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More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004
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STATUS
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approved
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