%I #20 Apr 20 2024 10:48:41

%S 1,101,10001,1010101,101101101,10101010101,1010010100101,

%T 101010101010101,10101101010110101,1010101010101010101,

%U 101010010101010010101,10101010101010101010101,1010101101010101011010101,101010101010101010101010101,10101010010101010101001010101

%N 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 a(n) is also A153499(n) written in base 2.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (101,-1110,102010,-111000,1010000,-1000000).

%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), n>7. [_R. J. Mathar_, Feb 20 2009]

%F 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 n ............ a(n)

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

%e 2 ............ 101

%e 3 ........... 10001

%e 4 .......... 1010101

%e 5 ......... 101101101

%e 6 ........ 10101010101

%e 7 ....... 1010010100101

%e 8 ...... 101010101010101

%e 9 ..... 10101101010110101

%e 10 ... 1010101010101010101

%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 ... /././.|.|.|.|.\.\.\

%Y Cf. A135577, A138146, A152576, A152764, A153497, A153498, A153499, 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 26 2010

%E More terms from _Colin Barker_, Sep 17 2013