A152764 -id:A152764 - cp's OEIS frontend

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

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

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

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

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).

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

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)

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

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

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.

Original entry on oeis.org

1, 101, 10001, 1010101, 101101101, 10101010101, 1010010100101, 101010101010101, 10101101010110101, 1010101010101010101, 101010010101010010101, 10101010101010101010101, 1010101101010101011010101, 101010101010101010101010101, 10101010010101010101001010101

Offset: 1

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

a(n) is also A153499(n) written in base 2.

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

Index entries for linear recurrences with constant coefficients, signature (101,-1110,102010,-111000,1010000,-1000000).

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

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]

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

A152766 Largest proper divisor of the Catalan number A000108(n).

Original entry on oeis.org

1, 1, 7, 21, 66, 143, 715, 2431, 8398, 29393, 104006, 371450, 1337220, 3231615, 17678835, 64822395, 238819350, 883631595, 3282060210, 12233133510, 45741281820, 171529806825, 644952073662, 2430973200726, 9183676536076, 34766775458002, 131873975875180

Offset: 2

Omar E. Pol, Dec 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 2..1669

Cf. A000108, A152761, A152762, A152763, A152764, A152765.

Divisors[CatalanNumber[#]][[-2]]&/@Range[2,40] (* Harvey P. Dale, Jun 13 2011 *)

a(n) = A032742(A000108(n)). - Amiram Eldar, Dec 01 2019

Edited and extended by N. J. A. Sloane, Dec 19 2008

cp's OEIS Frontend

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

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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.

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A152766 Largest proper divisor of the Catalan number A000108(n).

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