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A138145 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.

%I A138145 #18 Aug 09 2024 02:18:59
%S A138145 1,11,111,1111,11111,111111,1110111,11100111,111000111,1110000111,
%T A138145 11100000111,111000000111,1110000000111,11100000000111,
%U A138145 111000000000111,1110000000000111,11100000000000111,111000000000000111
%N A138145 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.
%C A138145 a(n) is also A147596(n) written in base 2. - _Omar E. Pol_, Nov 08 2008
%H A138145 Paolo Xausa, <a href="/A138145/b138145.txt">Table of n, a(n) for n = 1..995</a>
%H A138145 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A138145 From _Colin Barker_, Sep 15 2013: (Start)
%F A138145 a(n) = 111+111*10^(n-3) for n>5.
%F A138145 a(n) = 11*a(n-1)-10*a(n-2).
%F A138145 G.f.: -x*(10*x^2-1)*(100*x^4+10*x^2+1) / ((x-1)*(10*x-1)). (End)
%e A138145 n .... a(n)
%e A138145 1 .... 1
%e A138145 2 .... 11
%e A138145 3 .... 111
%e A138145 4 .... 1111
%e A138145 5 .... 11111
%e A138145 6 .... 111111
%e A138145 7 .... 1110111
%e A138145 8 .... 11100111
%e A138145 9 .... 111000111
%e A138145 10 ... 1110000111
%e A138145 11 ... 11100000111
%e A138145 12 ... 111000000111
%e A138145 13 ... 1110000000111
%t A138145 Table[If[n < 7, (10^n - 1)/9, 111 + 111*10^(n-3)], {n, 25}] (* or *)
%t A138145 LinearRecurrence[{11, -10}, {1, 11, 111, 1111, 11111, 111111, 1110111}, 25] (* _Paolo Xausa_, Aug 08 2024 *)
%o A138145 (PARI) Vec(-x*(10*x^2-1)*(100*x^4+10*x^2+1)/((x-1)*(10*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 15 2013
%Y A138145 Cf. A000533, A138144.
%Y A138145 Cf. A138118, A138119, A138120, A138146, A138721, A138826, A147596. [From _Omar E. Pol_, Nov 08 2008]
%K A138145 easy,nonn,base
%O A138145 1,2
%A A138145 _Omar E. Pol_, Mar 29 2008
%E A138145 Better definition from _Omar E. Pol_, Nov 16 2008