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A153500 First 3 terms coincide with A152756. For n>3, a(n) is the palindromic number formed from concatenation of 1, 0, A147759(n-3), 0, A147759(n-3), 0 and 1.

%I A153500 #20 Apr 20 2024 10:48:41
%S A153500 1,101,10001,1010101,101101101,10101010101,1010010100101,
%T A153500 101010101010101,10101101010110101,1010101010101010101,
%U A153500 101010010101010010101,10101010101010101010101,1010101101010101011010101,101010101010101010101010101,10101010010101010101001010101
%N A153500 First 3 terms coincide with A152756. For n>3, a(n) is the palindromic number formed from concatenation of 1, 0, A147759(n-3), 0, A147759(n-3), 0 and 1.
%C A153500 a(n) is also A153499(n) written in base 2.
%H A153500 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (101,-1110,102010,-111000,1010000,-1000000).
%F A153500 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), n>7. [_R. J. Mathar_, Feb 20 2009]
%F A153500 G.f.: -x*(1000000*x^6-1010000*x^5+10000*x^4-10100*x^3-910*x^2-1) / ((x-1)*(100*x-1)*(10*x^2+1)*(1000*x^2+1)). [_Colin Barker_, Sep 17 2013]
%e A153500 n ............ a(n)
%e A153500 1 ............. 1
%e A153500 2 ............ 101
%e A153500 3 ........... 10001
%e A153500 4 .......... 1010101
%e A153500 5 ......... 101101101
%e A153500 6 ........ 10101010101
%e A153500 7 ....... 1010010100101
%e A153500 8 ...... 101010101010101
%e A153500 9 ..... 10101101010110101
%e A153500 10 ... 1010101010101010101
%e A153500 ======================================
%e A153500 Another visualization of the structure
%e A153500 ======================================
%e A153500 1 ............. *
%e A153500 2 ............ /.\
%e A153500 3 ........... /...\
%e A153500 4 .......... /.*.*.\
%e A153500 5 ......... /./|.|\.\
%e A153500 6 ........ /./.|.|.\.\
%e A153500 7 ....... /./..|.|..\.\
%e A153500 8 ...... /./.*.|.|.*.\.\
%e A153500 9 ..... /././|.|.|.|\.\.\
%e A153500 10 ... /././.|.|.|.|.\.\.\
%Y A153500 Cf. A135577, A138146, A152576, A152764, A153497, A153498, A153499, A144564.
%K A153500 easy,base,nonn
%O A153500 1,2
%A A153500 _Omar E. Pol_, Dec 27 2008, Feb 18 2009
%E A153500 More terms from _R. J. Mathar_, Feb 20 2009
%E A153500 Keyword:base added by _Charles R Greathouse IV_, Apr 26 2010
%E A153500 More terms from _Colin Barker_, Sep 17 2013