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A147759
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Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1's and 0's.
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7
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1, 11, 101, 1001, 10101, 101101, 1010101, 10100101, 101010101, 1010110101, 10101010101, 101010010101, 1010101010101, 10101011010101, 101010101010101, 1010101001010101, 10101010101010101, 101010101101010101
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = 11*a(n-1)-20*a(n-2)+110*a(n-3)-100*a(n-4). G.f.: x/((1-x)*(1-10*x)*(1+10*x^2)). [R. J. Mathar, Feb 20 2009]
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EXAMPLE
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n .... Successive digits of a(n)
1 ............. ( 1 )
2 ............ ( 1 1 )
3 ........... ( 1 0 1 )
4 .......... ( 1 0 0 1 )
5 ......... ( 1 0 1 0 1 )
6 ........ ( 1 0 1 1 0 1 )
7 ....... ( 1 0 1 0 1 0 1 )
8 ...... ( 1 0 1 0 0 1 0 1 )
9 ..... ( 1 0 1 0 1 0 1 0 1 )
10 ... ( 1 0 1 0 1 1 0 1 0 1 )
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MATHEMATICA
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CoefficientList[Series[1/((1 - x) (1 - 10 x) (1 + 10 x^2)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 05 2015 *)
LinearRecurrence[{11, -20, 110, -100}, {1, 11, 101, 1001}, 30] (* Harvey P. Dale, Apr 10 2022 *)
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PROG
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(PARI) Vec(x/((1-x)*(1-10*x)*(1+10*x^2)) + O(x^30)) \\ Michel Marcus, Dec 05 2015
(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
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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