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A147759 Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1's and 0's.

%I A147759 #35 Oct 13 2024 07:09:03
%S A147759 1,11,101,1001,10101,101101,1010101,10100101,101010101,1010110101,
%T A147759 10101010101,101010010101,1010101010101,10101011010101,
%U A147759 101010101010101,1010101001010101,10101010101010101,101010101101010101
%N A147759 Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1's and 0's.
%C A147759 a(k(n)) is divisible by 3 iff k(n) is defined by k(1) = 5 and k(n+1) - k(n) =  A100285(n+2). - _Altug Alkan_, Dec 05 2015
%H A147759 Matthew Schulz, <a href="/A147759/b147759.txt">Table of n, a(n) for n = 1..1000</a>
%H A147759 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-20,110,-100).
%F A147759 From _R. J. Mathar_, Feb 20 2009: (Start)
%F A147759 a(n) = 11*a(n-1)-20*a(n-2)+110*a(n-3)-100*a(n-4).
%F A147759 G.f.: x/((1-x)*(1-10*x)*(1+10*x^2)). (End)
%F A147759 E.g.f.: (exp(x)*(10*exp(9*x) - 1) - 9*cos(sqrt(10)*x))/99. - _Stefano Spezia_, Oct 12 2024
%e A147759 n .... Successive digits of a(n)
%e A147759 1 ............. ( 1 )
%e A147759 2 ............ ( 1 1 )
%e A147759 3 ........... ( 1 0 1 )
%e A147759 4 .......... ( 1 0 0 1 )
%e A147759 5 ......... ( 1 0 1 0 1 )
%e A147759 6 ........ ( 1 0 1 1 0 1 )
%e A147759 7 ....... ( 1 0 1 0 1 0 1 )
%e A147759 8 ...... ( 1 0 1 0 0 1 0 1 )
%e A147759 9 ..... ( 1 0 1 0 1 0 1 0 1 )
%e A147759 10 ... ( 1 0 1 0 1 1 0 1 0 1 )
%t A147759 CoefficientList[Series[x/((1 - x) (1 - 10 x) (1 + 10 x^2)),{x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 05 2015 *)
%t A147759 LinearRecurrence[{11,-20,110,-100},{1,11,101,1001},30] (* _Harvey P. Dale_, Apr 10 2022 *)
%o A147759 (PARI) Vec(x/((1-x)*(1-10*x)*(1+10*x^2)) + O(x^30)) \\ _Michel Marcus_, Dec 05 2015
%o A147759 (Magma) I:=[1,11,101,1001]; [n le 4 select I[n] else 11*Self(n-1)-20*Self(n-2)+110*Self(n-3)-100*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 05 2015
%Y A147759 Cf. A000533, A094028, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147757.
%K A147759 base,easy,nonn
%O A147759 1,2
%A A147759 _Omar E. Pol_, Nov 11 2008