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A239933 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-1). 16
2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 14, 6, 6, 14, 16, 16, 18, 12, 18, 20, 8, 8, 20, 22, 22, 24, 24, 26, 10, 10, 26, 28, 8, 8, 28, 30, 30, 32, 12, 16, 12, 32, 34, 34, 36, 36, 38, 24, 24, 38, 40, 40, 42, 42, 44, 16, 16, 44, 46, 20, 46, 48, 12, 12, 48, 50, 18, 20, 18, 50, 52, 52, 54, 54, 56, 20, 20, 56, 58, 14, 14, 58, 60, 12, 12, 60, 62, 22, 22, 62, 64, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row n is a palindromic composition of sigma(4n-1).

Row n is also the row 4n-1 of A237270.

Row n has length A237271(4n-1).

Row sums give A239053.

Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the third 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-2), see A239932.

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..95.

EXAMPLE

The irregular triangle begins:

2, 2;

4, 4;

6, 6;

8, 8, 8;

10, 10;

12, 12;

14, 6, 6, 14;

16, 16;

18, 12, 18;

20, 8, 8, 20;

22, 22;

24, 24;

26, 10, 10, 26;

28, 8, 8, 28;

30, 30;

32, 12, 16, 12, 32;

...

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

.     _       _       _       _       _       _       _       _

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

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

.    | |     | |     | |     | |     | |     | |     | |    2  |_ _|

.    | |     | |     | |     | |     | |     | |     |_|_     2

.    | |     | |     | |     | |     | |     | |    4    |_

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

.    | |     | |     | |     | |     | |    6      |_      |_ _ _ _|

.    | |     | |     | |     | |     |_|_ _ _        |_   4

.    | |     | |     | |     | |    8      | |_ _      |

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

.    | |     | |     | |   10        |       |_  |_    |_ _ _ _ _ _|

.    | |     | |     |_|_ _ _ _      |_ _   8  |_ _|  6

.    | |     | |   12          |         |_        |

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

.    | |   14          | |         |_      |_ _    |_ _ _ _ _ _ _ _|

.    |_|_ _ _ _ _      | |_ _        |_        |  8

.  16            |     |_ _  |         |       |

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

.                |_ _     6    |_ _        |   |_ _ _ _ _ _ _ _ _ _|

.                    |         |_  |       | 10

.                    |_       6  | |_ _    |

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

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

.                            |         | 12

.                            |_ _ _    |

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

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

.                                  | 14

.                                  |

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

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

.                                16

.

For n = 7 we have that 4*7-1 = 27 and the 27th row of A237593 is [14, 5, 3, 2, 1, 2, 2, 1, 2, 3, 5, 14] and the 26th row of A237593 is [14, 5, 2, 2, 2, 1, 1, 2, 2, 2, 5, 14] therefore between both Dyck paths there are four regions (or parts) of sizes [14, 6, 6, 14], so row 7 is [14, 6, 6, 14].

The sum of divisors of 27 is 1 + 3 + 9 + 27 = A000203(27) = 40. On the other hand the sum of the parts of the symmetric representation of sigma(27) is 14 + 6 + 6 + 14 = 40, equaling the sum of divisors of 27.

CROSSREFS

Cf. A000203, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239932, A239934, A244050, A245092, A262626.

Sequence in context: A004079 A096494 A116568 * A061106 A319399 A161764

Adjacent sequences:  A239930 A239931 A239932 * A239934 A239935 A239936

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Mar 29 2014

STATUS

approved

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Last modified September 15 20:42 EDT 2019. Contains 327087 sequences. (Running on oeis4.)