%I #20 Nov 27 2016 09:07:39
%S 1,111,11111,1110111,111000111,11100000111,1110000000111,
%T 111000000000111,11100000000000111,1110000000000000111,
%U 111000000000000000111,11100000000000000000111
%N Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.
%C Bisection of A138145.
%C a(n) is also A147597(n) written in base 2. [_Omar E. Pol_, Nov 08 2008]
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F From _Colin Barker_, Sep 16 2013: (Start)
%F a(n) = 111 + 111*100^(n-2) for n>3.
%F a(n) = 101*a(n-1) - 100*a(n-2) for n>5.
%F G.f.: -x*(10*x-1)*(10*x+1)*(100*x^2+10*x+1) / ((x-1)*(100*x-1)). (End)
%e n ............ a(n)
%e 1 ............. 1
%e 2 ............ 111
%e 3 ........... 11111
%e 4 .......... 1110111
%e 5 ......... 111000111
%e 6 ........ 11100000111
%e 7 ....... 1110000000111
%e 8 ...... 111000000000111
%e 9 ..... 11100000000000111
%e 10 ... 1110000000000000111
%t Table[FromDigits@ If[n < 4, ConstantArray[1, 2 n - 1], Join[#, ConstantArray[0, 2 n - 7], #]] &@ ConstantArray[1, 3], {n, 14}] (* or *)
%t Rest@ CoefficientList[Series[-x (10 x - 1) (10 x + 1) (100 x^2 + 10 x + 1)/((x - 1) (100 x - 1)), {x, 0, 14}], x] (* _Michael De Vlieger_, Nov 25 2016 *)
%o (PARI) Vec(-x*(10*x-1)*(10*x+1)*(100*x^2+10*x+1)/((x-1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 16 2013
%Y Cf. A138144, A138145.
%Y Cf. A138118, A138119, A138120, A138721, A138826, A147597. [_Omar E. Pol_, Nov 08 2008]
%K easy,nonn,base
%O 1,2
%A _Omar E. Pol_, Mar 29 2008, May 18 2008
%E Better definition from _Omar E. Pol_, Nov 16 2008
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