VOOZH about

URL: https://oeis.org/A153500

⇱ A153500 - OEIS

login
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.
4
1, 101, 10001, 1010101, 101101101, 10101010101, 1010010100101, 101010101010101, 10101101010110101, 1010101010101010101, 101010010101010010101, 10101010101010101010101, 1010101101010101011010101, 101010101010101010101010101, 10101010010101010101001010101
OFFSET
1,2
COMMENTS
a(n) is also A153499(n) written in base 2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (101,-1110,102010,-111000,1010000,-1000000).
FORMULA
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]
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]
a(n) = A007088(A153499(n)). - Michel Marcus, Nov 28 2025
EXAMPLE
n ............ a(n)
1 ............. 1
2 ............ 101
3 ........... 10001
4 .......... 1010101
5 ......... 101101101
6 ........ 10101010101
7 ....... 1010010100101
8 ...... 101010101010101
9 ..... 10101101010110101
10 ... 1010101010101010101
======================================
Another visualization of the structure
======================================
1 ............. *
2 ............ /.\
3 ........... /...\
4 .......... /.*.*.\
5 ......... /./|.|\.\
6 ........ /./.|.|.\.\
7 ....... /./..|.|..\.\
8 ...... /./.*.|.|.*.\.\
9 ..... /././|.|.|.|\.\.\
10 ... /././.|.|.|.|.\.\.\
MATHEMATICA
LinearRecurrence[{101, -1110, 102010, -111000, 1010000, -1000000}, {1, 101, 10001, 1010101, 101101101, 10101010101, 1010010100101}, 20] (* Paolo Xausa, Nov 28 2025 *)
KEYWORD
easy,base,nonn
AUTHOR
Omar E. Pol, Dec 27 2008, Feb 18 2009
EXTENSIONS
More terms from R. J. Mathar, Feb 20 2009
Keyword:base added by Charles R Greathouse IV, Apr 26 2010
More terms from Colin Barker, Sep 17 2013
STATUS
approved