A153500 - OEIS

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

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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

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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

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