A086577 - OEIS

%I #29 Sep 12 2024 18:49:48

%S 0,54,594,5994,59994,599994,5999994,59999994,599999994,5999999994,

%T 59999999994,599999999994,5999999999994,59999999999994,

%U 599999999999994,5999999999999994,59999999999999994,599999999999999994,5999999999999999994,59999999999999999994,599999999999999999994

%N a(n) = 6*(10^n - 1).

%C Original definition: a(n) = k where R(k+6) = 6.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 6*9*A002275(n) = 6*A002283(n).

%F R(a(n)) = A086576(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.: 54*x/((1 - x)*(1 - 10*x)). (End)

%F E.g.f.: 6*exp(x)*(exp(9*x) - 1). - _Elmo R. Oliveira_, Sep 12 2024

%t LinearRecurrence[{11,-10},{0,54},30] (* _Harvey P. Dale_, Nov 27 2022 *)

%Y Cf. A002275, A004086 (R(n)).

%Y One of a family of sequences of the form "Numbers k such that reverse(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,easy

%O 0,2

%A _Ray Chandler_, Jul 22 2003

%E Name edited by _Jinyuan Wang_, Aug 04 2021