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

1, 111, 10101, 1001001, 101010101, 10110101101, 1010101010101, 101001010100101, 10101010101010101, 1010110101010110101, 101010101010101010101, 10101001010101010010101

Offset: 1

Author

Omar E. Pol, Dec 27 2008, Feb 18 2009

Keywords

• easy
• base
• nonn

Comments

a(n) is also A153497(n) written in base 2.

Examples

			n ............. a(n)
1 .............. 1
2 ............. 111
3 ............ 10101
4 ........... 1001001
5 .......... 101010101
6 ......... 10110101101
7 ........ 1010101010101
8 ....... 101001010100101
9 ...... 10101010101010101
10 .... 1010110101010110101
11 ... 101010101010101010101
======================================
Another visualization of the structure
======================================
1 .............. *
2 ............. /|\
3 ............ /.|.\
4 ........... /..|..\
5 .......... /.*.|.*.\
6 ......... /./|.|.|\.\
7 ........ /./.|.|.|.\.\
8 ....... /./..|.|.|..\.\
9 ...... /./.*.|.|.|.*.\.\
10 .... /././|.|.|.|.|\.\.\
11 ... /././.|.|.|.|.|.\.\.\
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (101, -1110, 102010, -111000, 1010000, -1000000).

Crossrefs

Cf. A135577, A138146, A152576, A152764, A153497, A153499, A153500, A144564.

Formula

From R. J. Mathar, Feb 20 2009: (Start)

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).

G.f.: x(1+10x+2000x^3-91000*x^4+100000x^5)/((1-100x)(1-x)(1+10x^2)(1+1000x^2)). (End)

Extensions

More terms from R. J. Mathar, Feb 20 2009

Keyword:base added by Charles R Greathouse IV, Apr 23 2010