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%I #33 Aug 04 2021 07:42:26
%S 0,45,495,4995,49995,499995,4999995,49999995,499999995,4999999995,
%T 49999999995,499999999995,4999999999995,49999999999995,
%U 499999999999995,4999999999999995,49999999999999995,499999999999999995,4999999999999999995,49999999999999999995,499999999999999999995
%N a(n) = 5*(10^n - 1).
%C Original definition: a(n) = k where R(k+5) = 5.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F a(n) = 5*9*A002275(n) = 5*A002283(n).
%F R(a(n)) = A086577(n).
%F From _Chai Wah Wu_, Jul 08 2016: (Start)
%F a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
%F G.f.: 45*x/((1 - x)*(1 - 10*x)). (End)
%e From _John Elias_, Jun 23 2021: (Start)
%e 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45;
%e 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495;
%e 111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 = 4995;
%e 1111 + 2222 + 3333 + 4444 + 5555 + 6666 + 7777 + 8888 + 9999 = 49995;
%e 11111 + 22222 + 33333 + 44444 + 55555 + 66666 + 77777 + 88888 + 99999 = 499995; etc. (End)
%t Join[{0}, LinearRecurrence[{11,-10},{45,495},50]] (* _G. C. Greubel_, Jul 08 2016 *)
%Y Cf. A002275, A002283, A004086 (R(n)).
%Y One of family of sequences of form a(n)=k, where R(k+m)=m, m = 1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.
%K nonn,base
%O 0,2
%A _Ray Chandler_, Jul 22 2003
%E Name edited by _Jinyuan Wang_, Aug 04 2021
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