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.

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

Table of n, a(n) for n=1..15.

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]

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

Crossrefs

Cf. A135577, A138146, A152576, A152764, A153497, A153498, A153499, A144564.

Sequence in context: A303572 A152756 A265172 * A262861 A371563 A164367

Adjacent sequences: A153497 A153498 A153499 * A153501 A153502 A153503

Keyword

easy,base,nonn,changed

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