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A239932 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-2). 17
3, 12, 9, 9, 12, 12, 39, 18, 18, 21, 21, 72, 27, 27, 30, 30, 96, 36, 36, 39, 15, 39, 120, 45, 45, 48, 48, 144, 54, 36, 54, 57, 57, 84, 84, 63, 63, 66, 66, 234, 72, 72, 75, 21, 75, 108, 108, 81, 81, 84, 48, 84, 120, 120, 90, 90, 93, 93, 312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row n is a palindromic composition of sigma(4n-2).

Row n is also the row 4n-2 of A237270.

Row n has length A237271(4n-2).

Row sums give A239052.

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

For the parts of the symmetric representation of sigma(4n-3), see A239931.

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..59.

EXAMPLE

The irregular triangle begins:

3;

12;

9, 9;

12, 12;

39;

18, 18;

21, 21;

72;

27, 27;

30, 30;

96;

36, 36;

39, 15, 39;

120;

45, 45;

48, 48;

...

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

.                                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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

.                                | |

.                                | |

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

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

.                          |       | | |

.                       _ _|  _ _ _| | |

.                  72 _|     |       | |  _ _ _ _ _ _ _ _ _ _ _ _

.                   _|      _| 21 _ _| | |  _ _ _ _ _ _ _ _ _ _ _|

.                  |      _|     |_ _ _| | |

.               _ _|    _|    _ _|       | |

.              |    _ _|    _|     18 _ _| |  _ _ _ _ _ _ _ _ _ _

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

.     _ _ _ _ _|   | 21 _ _|        _|       | |

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

.    | |      _ _ _ _ _| | 18 _ _|       |     |  _ _ _ _ _ _ _ _

.    | |     |  _ _ _ _ _|   | |     39 _|  _ _| |  _ _ _ _ _ _ _|

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

.    | |     | |     |  _ _ _ _|   |    _|   12 _| |

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

.    | |     | |     | |     |  _ _ _ _| 12 _ _|     |  _ _ _ _ _|

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

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

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

.    | |     | |     | |     | |     | |     |  _ _| 12 _|  _ _ _|

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

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

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

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

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

.

For n = 7 we have that 4*7-2 = 26 and the 26th row of A237593 is [14, 5, 2, 2, 2, 1, 1, 2, 2, 2, 5, 14] and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] therefore between both Dyck paths there are two regions (or parts) of sizes [21, 21], so row 7 is [21, 21].

The sum of divisors of 26 is 1 + 2 + 13 + 26 = A000203(26) = 42. On the other hand the sum of the parts of the symmetric representation of sigma(26) is 21 + 21 = 42, equaling the sum of divisors of 26.

CROSSREFS

Cf. A000203, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239052, A239660, A239931, A239933, A239934, A244050, A245092, A262626.

Sequence in context: A234947 A051353 A070706 * A114237 A060035 A165988

Adjacent sequences:  A239929 A239930 A239931 * A239933 A239934 A239935

KEYWORD

nonn,tabf,more

AUTHOR

Omar E. Pol, Mar 29 2014

STATUS

approved

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)