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%I #13 Oct 12 2017 18:17:38
%S 2,30,382,4550,52062,579670,6328142,68064390,723690622,7624326710,
%T 79730051502,828681574630,8569245282782,88234318656150,
%U 905219979016462,9258090922259270,94433929411444542,961016475814111990
%N a(n) = ((10^n - 1) - 9^n)/9.
%C 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.
%H Matthew House, <a href="/A083446/b083446.txt">Table of n, a(n) for n = 2..996</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-109,90).
%F G.f.: 2*x^2*(1-5*x)/((1-x)*(1-9*x)*(1-10*x)).
%F a(n) = 20*a(n-1) - 109*a(n-2) + 90*a(n-3). - _Matthew House_, Jan 16 2017
%e a(4) = (9999 - 9*9*9*9)/9 = 382.
%t LinearRecurrence[{20,-109,90},{2,30,382},20] (* _Harvey P. Dale_, Oct 12 2017 *)
%o (PARI) for (i=2,30,print1(((10^n -1) - 9^n)/9,","))))
%Y Cf. A083445.
%K base,easy,nonn
%O 2,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003
%E More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004
%E Edited by _Jon E. Schoenfield_, Jan 16 2017
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