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A153498 Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit. 3

%I

%S 1,111,10101,1001001,101010101,10110101101,1010101010101,

%T 101001010100101,10101010101010101,1010110101010110101,

%U 101010101010101010101,10101001010101010010101

%N Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit.

%C a(n) is also A153497(n) written in base 2.

%F a(n)=101*a(n-1)-1110*a(n-2)+102010*a(n-3)-111000*a(n-4)+1010000*a(n-5)-1000000*a(n-6). G.f.: x(1+10x+2000x^3-91000*x^4+100000x^5)/((1-100x)(1-x)(1+10x^2)(1+1000x^2)). [From _R. J. Mathar_, Feb 20 2009]

%e n ............. a(n)

%e 1 .............. 1

%e 2 ............. 111

%e 3 ............ 10101

%e 4 ........... 1001001

%e 5 .......... 101010101

%e 6 ......... 10110101101

%e 7 ........ 1010101010101

%e 8 ....... 101001010100101

%e 9 ...... 10101010101010101

%e 10 .... 1010110101010110101

%e 11 ... 101010101010101010101

%e ======================================

%e Another visualization of the structure

%e ======================================

%e 1 .............. *

%e 2 ............. /|\

%e 3 ............ /.|.\

%e 4 ........... /..|..\

%e 5 .......... /.*.|.*.\

%e 6 ......... /./|.|.|\.\

%e 7 ........ /./.|.|.|.\.\

%e 8 ....... /./..|.|.|..\.\

%e 9 ...... /./.*.|.|.|.*.\.\

%e 10 .... /././|.|.|.|.|\.\.\

%e 11 ... /././.|.|.|.|.|.\.\.\

%Y Cf. A135577, A138146, A152576, A152764, A153497, A153499, A153500, A144564.

%K easy,base,nonn

%O 1,2

%A _Omar E. Pol_, Dec 27 2008, Feb 18 2009

%E More terms from _R. J. Mathar_, Feb 20 2009

%E Keyword:base added by _Charles R Greathouse IV_, Apr 23 2010

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)