A279388 - OEIS

A279388

Irregular triangle read by rows: T(n,k) is the sum of the subparts in the k-th layer of the symmetric representation of sigma(n), if such a layer exists.

1, 3, 4, 7, 6, 11, 1, 8, 15, 13, 18, 12, 23, 5, 14, 24, 23, 1, 31, 18, 35, 4, 20, 39, 3, 32, 36, 24, 47, 13, 31, 42, 40, 55, 1, 30, 59, 13, 32, 63, 48, 54, 45, 3, 71, 20, 38, 60, 56, 79, 11, 42, 83, 13, 44, 84, 73, 5, 72, 48, 95, 29, 57, 93, 72, 98, 54, 107, 13, 72, 111, 9, 80, 90, 60, 119, 37, 12

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..78.

Index entries for sequences related to sigma(n)

EXAMPLE

Triangle begins (first 15 rows):

11, 1;

15;

13;

18;

12;

23, 5;

14;

24;

23, 1;

...

For n = 12 we have that the 11th row of triangle A237593 is [6, 3, 1, 1, 1, 1, 3, 6] and the 12th row of the same triangle is [7, 2, 2, 1, 1, 2, 2, 7], so the diagram of the symmetric representation of sigma(12) = 28 is constructed as shown below in Figure 1:

. _ _

. | | | |

. _ _ _| | _ _ _| |

. 28 _| _ _| 23 _| _ _ _|

. _| | _| _| |

. | _| | _| _|

. | _ _| | |_ _|

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

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

. Figure 1. The symmetric Figure 2. After the dissection

. representation of sigma(12) of the symmetric representation

. has only one part which of sigma(12) into layers of

. contains 28 cells, so width 1 we can see two "subparts"

. A000203(12) = 28. that contain 23 and 5 cells

. respectively, so the 12th row of

. this triangle is [23, 5].

For n = 15 we have that the 14th row of triangle A237593 is [8, 3, 1, 2, 2, 1, 3, 8] and the 15th row of the same triangle is [8, 3, 2, 1, 1, 1, 1, 2, 3, 8], so the diagram of the symmetric representation of sigma(15) is constructed as shown below in Figure 3:

. _ _

. | | | |

. 8 | | 8 | |

. | | | |

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

. 8 _ _| | 7 _ _| |

. | _| | _ _|

. _| _| _| |_|

. |_ _| |_ _| 1

. 8 | 8 |

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

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

. Figure 3. The symmetric Figure 4. After the dissection

. representation of sigma(15) of the symmetric representation

. has three parts of size 8, of sigma(15) into layers of

. whose sum is 8 + 8 + 8 = 24, width 1 we can see four "subparts".

. so A000203(15) = 24. The first layer has three subparts

. whose sum is 8 + 7 + 8 = 23. The

. second layer has only one subpart

. of size 1, so the 15th row of this

. triangle is [23, 1].

CROSSREFS

For the definition of "subparts" see A279387.

For the triangle of subparts see A279391.

Row sums give A000203.

Row n has length A250068(n).

Cf. A001227, A005279, A196020, A235791, A236104, A237048, A237270, A237591, A237593, A239657, A244050, A245092, A250070, A261699, A262626.

Sequence in context: A126253 A057032 A347529 * A292288 A347273 A355584

Adjacent sequences: A279385 A279386 A279387 * A279389 A279390 A279391

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Dec 12 2016

STATUS

approved