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

%I A153498 #17 Oct 16 2024 11:31:52
%S A153498 1,111,10101,1001001,101010101,10110101101,1010101010101,
%T A153498 101001010100101,10101010101010101,1010110101010110101,
%U A153498 101010101010101010101,10101001010101010010101
%N A153498 Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit.
%C A153498 a(n) is also A153497(n) written in base 2.
%H A153498 Ray Chandler, <a href="/A153498/b153498.txt">Table of n, a(n) for n = 1..500</a>
%H A153498 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (101, -1110, 102010, -111000, 1010000, -1000000).
%F A153498 From _R. J. Mathar_, Feb 20 2009: (Start)
%F A153498 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).
%F A153498 G.f.: x(1+10x+2000x^3-91000*x^4+100000x^5)/((1-100x)(1-x)(1+10x^2)(1+1000x^2)). (End)
%e A153498 n ............. a(n)
%e A153498 1 .............. 1
%e A153498 2 ............. 111
%e A153498 3 ............ 10101
%e A153498 4 ........... 1001001
%e A153498 5 .......... 101010101
%e A153498 6 ......... 10110101101
%e A153498 7 ........ 1010101010101
%e A153498 8 ....... 101001010100101
%e A153498 9 ...... 10101010101010101
%e A153498 10 .... 1010110101010110101
%e A153498 11 ... 101010101010101010101
%e A153498 ======================================
%e A153498 Another visualization of the structure
%e A153498 ======================================
%e A153498 1 .............. *
%e A153498 2 ............. /|\
%e A153498 3 ............ /.|.\
%e A153498 4 ........... /..|..\
%e A153498 5 .......... /.*.|.*.\
%e A153498 6 ......... /./|.|.|\.\
%e A153498 7 ........ /./.|.|.|.\.\
%e A153498 8 ....... /./..|.|.|..\.\
%e A153498 9 ...... /./.*.|.|.|.*.\.\
%e A153498 10 .... /././|.|.|.|.|\.\.\
%e A153498 11 ... /././.|.|.|.|.|.\.\.\
%Y A153498 Cf. A135577, A138146, A152576, A152764, A153497, A153499, A153500, A144564.
%K A153498 easy,base,nonn
%O A153498 1,2
%A A153498 _Omar E. Pol_, Dec 27 2008, Feb 18 2009
%E A153498 More terms from _R. J. Mathar_, Feb 20 2009
%E A153498 Keyword:base added by _Charles R Greathouse IV_, Apr 23 2010