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A239931 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-3). 43
1, 3, 3, 5, 3, 5, 7, 7, 9, 9, 11, 5, 5, 11, 13, 5, 13, 15, 15, 17, 7, 7, 17, 19, 19, 21, 21, 23, 32, 23, 25, 7, 25, 27, 27, 29, 11, 11, 29, 31, 31, 33, 9, 9, 33, 35, 13, 13, 35, 37, 37, 39, 18, 39, 41, 15, 9, 15, 41, 43, 11, 11, 43, 45, 45, 47, 17, 17, 47, 49, 49, 51, 51, 53, 43, 43, 53, 55, 55, 57, 57, 59, 21, 22, 21, 59, 61, 11, 61, 63, 15, 15, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n is a palindromic composition of sigma(4n-3).

Row n is also the row 4n-3 of A237270.

Row n has length A237271(4n-3).

Row sums give A112610.

Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the first quadrant of the spiral described in A239660, see example.

For the parts of the symmetric representation of sigma(4n-2), see A239932.

For the parts of the symmetric representation of sigma(4n-1), see A239933.

For the parts of the symmetric representation of sigma(4n), see A239934.

We can find the spiral (mentioned above) on the terraces of the pyramid described in A244050. - Omar E. Pol, Dec 06 2016

LINKS

Table of n, a(n) for n=1..93.

EXAMPLE

The irregular triangle begins:

   1;

   3,  3;

   5,  3,  5;

   7,  7;

   9,  9;

  11,  5,  5, 11;

  13,  5, 13;

  15, 15;

  17,  7,  7, 17;

  19, 19;

  21, 21;

  23, 32, 23;

  25,  7, 25;

  27, 27;

  29, 11, 11, 29;

  31, 31;

  ...

Illustration of initial terms in the first quadrant of the spiral described in A239660:

.

.     _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15

.    |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

.                                  |

.                                  |

.     _ _ _ _ _ _ _ _ _ _ _ _ _ 13 |

.    |_ _ _ _ _ _ _ _ _ _ _ _ _|   |

.                              |   |_ _ _

.                              |         |

.     _ _ _ _ _ _ _ _ _ _ _ 11 |         |_

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

.                          |         |_ _ 5  |_

.                          |         |_  |_    |_ _

.     _ _ _ _ _ _ _ _ _ 9  |_ _ _      |_  |       |

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

.                      |       |_ _|_ 5      |     |_ _ _ _ _ _ 15

.                      |           | |_      |               | |

.     _ _ _ _ _ _ _ 7  |_ _        |_  |     |_ _ _ _ _ 13   | |

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

.                  |         |_      |_|_ _ _ _ 11   | |     | |

.                  |_ _        |             | |     | |     | |

.     _ _ _ _ _ 5      |_      |_ _ _ _ 9    | |     | |     | |

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

.              |_ _ 3    |_ _ _ 7    | |     | |     | |     | |

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

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

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

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

.            | |     | |     | |     | |     | |     | |     | |

.     _ 1    | |     | |     | |     | |     | |     | |     | |

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

.

For n = 7 we have that 4*7-3 = 25 and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] and the 24th row of A237593 is [13, 4, 3, 2, 1, 1, 1, 1, 2, 3, 4, 13] therefore between both Dyck paths there are three regions (or parts) of sizes [13, 5, 13], so row 7 is [13, 5, 13].

The sum of divisors of 25 is 1 + 5 + 25 = A000203(25) = 31. On the other hand the sum of the parts of the symmetric representation of sigma(25) is 13 + 5 + 13 = 31, equaling the sum of divisors of 25.

CROSSREFS

Cf. A000203, A112610, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239932-A239934, A244050, A245092, A262626.

Sequence in context: A131832 A255316 A078587 * A033558 A046217 A057662

Adjacent sequences:  A239928 A239929 A239930 * A239932 A239933 A239934

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Mar 29 2014

STATUS

approved

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Last modified October 19 03:20 EDT 2019. Contains 328211 sequences. (Running on oeis4.)