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A240020 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(2n-1). 4
1, 2, 2, 3, 3, 4, 4, 5, 3, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 5, 5, 11, 12, 12, 13, 5, 13, 14, 6, 6, 14, 15, 15, 16, 16, 17, 7, 7, 17, 18, 12, 18, 19, 19, 20, 8, 8, 20, 21, 21, 22, 22, 23, 32, 23, 24, 24, 25, 7, 25, 26, 10, 10, 26, 27, 27, 28, 8, 8, 28, 29, 11, 11, 29, 30, 30, 31, 31, 32, 12, 26, 12, 32, 33, 9, 9, 33, 34, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n lists the parts of the symmetric representation of A008438(n-1).

Also these are the parts from the odd-indexed rows of A237270.

Also these are the parts in the quadrants 1 and 3 of the spiral described in A239660, see example.

Row sums give A008438.

The length of row n is A237271(2n-1).

Both column 1 and the right border are equal to n.

Note that also the sequence can be represented in a quadrant.

We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016

LINKS

Table of n, a(n) for n=1..92.

EXAMPLE

1;

2, 2;

3, 3;

4, 4;

5, 3, 5;

6, 6;

7, 7;

8, 8, 8;

9, 9;

10, 10;

11, 5, 5, 11;

12, 12;

13, 5, 13;

14, 6, 6, 14;

15, 15;

16, 16;

17, 7, 7, 17;

18, 12, 18;

19, 19;

20, 8, 8, 20;

21, 21;

22, 22;

23, 32, 23;

24, 24;

25, 7, 25;

...

Illustration of initial terms (rows 1..8):

.

.                                   _ _ _ _ _ _ _ 7

.                                  |_ _ _ _ _ _ _|

.                                                |

.                                                |_ _

.                                   _ _ _ _ _ 5      |_

.                                  |_ _ _ _ _|         |

.                                            |_ _ 3    |_ _ _ 7

.                                            |_  |         | |

.                                   _ _ _ 3    |_|_ _ 5    | |

.                                  |_ _ _|         | |     | |

.                                        |_ _ 3    | |     | |

.                                          | |     | |     | |

.                                   _ 1    | |     | |     | |

.     _       _       _       _    |_|     |_|     |_|     |_|

.    | |     | |     | |     | |

.    | |     | |     | |     |_|_ _

.    | |     | |     | |    2  |_ _|

.    | |     | |     |_|_     2

.    | |     | |    4    |_

.    | |     |_|_ _        |_ _ _ _

.    | |    6      |_      |_ _ _ _|

.    |_|_ _ _        |_   4

.   8      | |_ _      |

.          |_    |     |_ _ _ _ _ _

.            |_  |_    |_ _ _ _ _ _|

.           8  |_ _|  6

.                  |

.                  |_ _ _ _ _ _ _ _

.                  |_ _ _ _ _ _ _ _|

.                 8

.

The figure shows the quadrants 1 and 3 of the spiral described in A239660.

For n = 5 we have that 2*5 - 1 = 9 and the 9th row of A237593 is [5, 2, 2, 2, 2, 5] and the 8th row of A237593 is [5, 2, 1, 1, 2, 5] therefore between both symmetric Dyck paths there are three regions (or parts) of sizes [5, 3, 5], so row 5 is [5, 3, 5], see the third arm of the spiral in the first quadrant.

The sum of divisors of 9 is 1 + 3 + 9 = A000203(9) = 13. On the other hand the sum of the parts of the symmetric representation of sigma(9) is 5 + 3 + 5 = 13, equaling the sum of divisors of 9.

CROSSREFS

Cf. A000203, A005408, A008438, A112610, A196020, A236104, A237048, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239933, A244050, A245092, A262626.

Sequence in context: A220032 A219773 A187446 * A336430 A167232 A319468

Adjacent sequences:  A240017 A240018 A240019 * A240021 A240022 A240023

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Mar 31 2014

STATUS

approved

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Last modified January 20 06:12 EST 2022. Contains 350467 sequences. (Running on oeis4.)