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%I #48 Nov 22 2023 22:29:09
%S 1,18,252,3168,37512,427608,4748472,51736248,555626232,5900636088,
%T 62105724792,648951523128,6740563708152,69665073373368,
%U 716985660360312,7352870943242808,75175838489185272,766582546402667448
%N Number of "9ish numbers" with n digits.
%C First difference of A016189. ("9" can be replaced by any other nonzero digit, however only the 9ish numbers are closed under lunar multiplication.)
%C See A257285 - A257289 for first differences of 5^n-4^n, ..., 9^n-8^n. These also give the number of n-digit numbers whose largest digit is 5, 6, 7, 8, respectively. - _M. F. Hasler_, May 04 2015
%H Stefano Spezia, <a href="/A088924/b088924.txt">Table of n, a(n) for n = 1..950</a>
%H D. Applegate, <a href="/A087061/a087061.txt">C program for lunar arithmetic and number theory</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H D. Applegate, M. LeBrun, and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19,-90).
%F a(n) = 9*10^(n-1) - 8*9^(n-1).
%F G.f.: x*(1 - x)/(1 - 19*x + 90*x^2). - _Bobby Milazzo_, May 02 2014
%F a(n) = 19*a(n-1) - 90*a(n-2). - _Vincenzo Librandi_, May 04 2015
%F E.g.f.: (81*exp(10*x) - 80*exp(9*x) - 1)/90. - _Stefano Spezia_, Nov 16 2023
%e a(2) = 18 because 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99 are the eighteen two-digit 9ish numbers.
%p A088924:=n->9*10^(n-1) - 8*9^(n-1); seq(A088924(n), n=1..30); # _Wesley Ivan Hurt_, May 15 2014
%t Series[(x (1 - x))/(1 - 19 x + 90 x^2), {x, 0, 10}] (* _Bobby Milazzo_, May 02 2014 *)
%t Table[9*10^(n - 1) - 8*9^(n - 1), {n, 30}] (* _Wesley Ivan Hurt_, May 15 2014 *)
%o (PARI) a(n)=9*10^n-8*9^n \\ _M. F. Hasler_, May 04 2015
%o (Magma) [9*10^(n-1) - 8*9^(n-1): n in [1..30]]; // _Vincenzo Librandi_, May 04 2015
%Y Cf. A016189, A011539, A257285, A257286, A257287, A257288, A257289.
%K base,easy,nonn
%O 1,2
%A _Marc LeBrun_, Oct 23 2003
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