A153498 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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).

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)

EXAMPLE

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

CROSSREFS

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

Sequence in context: A265280 A267275 A135577 * A118110 A267608 A244663

Adjacent sequences: A153495 A153496 A153497 * A153499 A153500 A153501

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 23 2010

STATUS

approved