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A002282 a(n) = 8*(10^n - 1)/9.

%I A002282 #64 Jul 21 2025 00:25:45
%S A002282 0,8,88,888,8888,88888,888888,8888888,88888888,888888888,8888888888,
%T A002282 88888888888,888888888888,8888888888888,88888888888888,
%U A002282 888888888888888,8888888888888888,88888888888888888,888888888888888888,8888888888888888888,88888888888888888888,888888888888888888888
%N A002282 a(n) = 8*(10^n - 1)/9.
%C A002282 If the initial term is omitted, might be called eightful (or hateful) numbers!
%D A002282 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 32.
%H A002282 Harry J. Smith, <a href="/A002282/b002282.txt">Table of n, a(n) for n = 0..200</a>
%H A002282 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A002282 From _Jaume Oliver Lafont_, Feb 03 2009: (Start)
%F A002282 a(n) = 11*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=8.
%F A002282 G.f.: 8*x/((1-x)*(1-10*x)). (End)
%F A002282 a(n) = A178635(n)/A002283(n). - _Reinhard Zumkeller_, May 31 2010
%F A002282 a(n) = a(n-1) + 8*10^(n-1), with a(0)=0. - _Vincenzo Librandi_, Jul 22 2010
%F A002282 a(n) = 8*A002275(n) = A002283(n) - A002275(n). - _Carauleanu Marc_, Sep 03 2016
%F A002282 From _Ilya Gutkovskiy_, Sep 03 2016: (Start)
%F A002282 E.g.f.: 8*(exp(9*x) - 1)*exp(x)/9.
%F A002282 a(n) = floor(8*10^n/9). (End)
%F A002282 From _Elmo R. Oliveira_, Jul 20 2025: (Start)
%F A002282 a(n) = (A246058(n) - 1)/2.
%F A002282 a(n) = A010785(A017257(n-1)) for n >= 1. (End)
%e A002282 Curious multiplications:
%e A002282 9*9 + 7 = 88;
%e A002282 98*9 + 6 = 888;
%e A002282 987*9 + 5 = 8888;
%e A002282 9876*9 + 4 = 88888;
%e A002282 98765*9 + 3 = 888888;
%e A002282 987654*9 + 2 = 8888888;
%e A002282 9876543*9 + 1 = 88888888;
%e A002282 98765432*9 + 0 = 888888888;
%e A002282 987654321*9 - 1 = 8888888888;
%e A002282 9876543210*9 - 2 = 88888888888. - _Philippe Deléham_, Mar 09 2014
%p A002282 A002282:=n->8*(10^n - 1)/9; seq(A002282(n), n=0..20); # _Wesley Ivan Hurt_, Mar 10 2014
%t A002282 LinearRecurrence[{11,-10}, {0,8}, 20] (* _Harvey P. Dale_, May 30 2013 *)
%o A002282 (PARI) { a=-4/5; for (n = 0, 200, a+=8*10^(n - 1); write("b002282.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jun 27 2009
%o A002282 (Python) def a(n): return 8*(10**n - 1)//9 # _Martin Gergov_, Oct 19 2022
%Y A002282 Cf. A002275, A002276, A002277, A002278, A002279, A002280, A002281, A002283, A059988, A075412, A178635.
%Y A002282 Cf. A010785, A017257, A051003, A059482, A246058.
%K A002282 easy,nonn
%O A002282 0,2
%A A002282 _N. J. A. Sloane_