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%I #23 Aug 02 2017 10:09:41
%S 1,11,101,1001,10101,101101,1011101,10111101,101111101,1011111101,
%T 10111111101,101111111101,1011111111101,10111111111101,
%U 101111111111101,1011111111111101,10111111111111101,101111111111111101
%N Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.
%C a(n) is also A147758(n) written in base 2.
%C a(A016789(n)) is divisible by 3 for n > 0. - _Altug Alkan_, Dec 06 2015
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F G.f.: x+11*x^2+101*x^3-91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ). - _R. J. Mathar_, Aug 24 2011
%F a(n) = 11*a(n-1) - 10*a(n-2) for n>2. _Wesley Ivan Hurt_, Dec 06 2015
%e n .... Successive digits of a(n)
%e 1 ............. ( 1 )
%e 2 ............ ( 1 1 )
%e 3 ........... ( 1 0 1 )
%e 4 .......... ( 1 0 0 1 )
%e 5 ......... ( 1 0 1 0 1 )
%e 6 ........ ( 1 0 1 1 0 1 )
%e 7 ....... ( 1 0 1 1 1 0 1 )
%e 8 ...... ( 1 0 1 1 1 1 0 1 )
%e 9 ..... ( 1 0 1 1 1 1 1 0 1 )
%e 10 ... ( 1 0 1 1 1 1 1 1 0 1 )
%t f[n_] := Block[{w = {1, 0}}, Which[n == 1, w = {1}, n == 2, w = {1, 1}, n == 3, AppendTo[w, 1], n >= 4, w = Join[w, Table[1, {n - 4}], Reverse@ w]]; FromDigits@ w]; Array[f, 19] (* _Michael De Vlieger_, Dec 05 2015 *)
%t LinearRecurrence[{11,-10},{1,11,101,1001,10101},20] (* _Harvey P. Dale_, Aug 02 2017 *)
%o (PARI) Vec( x+11*x^2+101*x^3 -91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ) + O(x^30)) \\ _Michel Marcus_, Dec 05 2015
%Y Cf. A000533, A016789, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147758.
%Y Cf. A144564 (a bisection).
%K base,easy,nonn
%O 1,2
%A _Omar E. Pol_, Nov 11 2008
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