cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A138146 Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.

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%I A138146 #20 Nov 27 2016 09:07:39
%S A138146 1,111,11111,1110111,111000111,11100000111,1110000000111,
%T A138146 111000000000111,11100000000000111,1110000000000000111,
%U A138146 111000000000000000111,11100000000000000000111
%N A138146 Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.
%C A138146 Bisection of A138145.
%C A138146 a(n) is also A147597(n) written in base 2. [_Omar E. Pol_, Nov 08 2008]
%H A138146 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A138146 From _Colin Barker_, Sep 16 2013: (Start)
%F A138146 a(n) = 111 + 111*100^(n-2) for n>3.
%F A138146 a(n) = 101*a(n-1) - 100*a(n-2) for n>5.
%F A138146 G.f.: -x*(10*x-1)*(10*x+1)*(100*x^2+10*x+1) / ((x-1)*(100*x-1)). (End)
%e A138146 n ............ a(n)
%e A138146 1 ............. 1
%e A138146 2 ............ 111
%e A138146 3 ........... 11111
%e A138146 4 .......... 1110111
%e A138146 5 ......... 111000111
%e A138146 6 ........ 11100000111
%e A138146 7 ....... 1110000000111
%e A138146 8 ...... 111000000000111
%e A138146 9 ..... 11100000000000111
%e A138146 10 ... 1110000000000000111
%t A138146 Table[FromDigits@ If[n < 4, ConstantArray[1, 2 n - 1], Join[#, ConstantArray[0, 2 n - 7], #]] &@ ConstantArray[1, 3], {n, 14}] (* or *)
%t A138146 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 A138146 (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 A138146 Cf. A138144, A138145.
%Y A138146 Cf. A138118, A138119, A138120, A138721, A138826, A147597. [_Omar E. Pol_, Nov 08 2008]
%K A138146 easy,nonn,base
%O A138146 1,2
%A A138146 _Omar E. Pol_, Mar 29 2008, May 18 2008
%E A138146 Better definition from _Omar E. Pol_, Nov 16 2008