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A302800 Irregular triangle read by rows: T(n,k) is the area of the k-th region of the diagram with n rows described in A237591. 0
1, 3, 5, 1, 8, 2, 11, 4, 15, 5, 1, 19, 7, 2, 24, 9, 3, 29, 11, 5, 35, 13, 6, 1, 41, 16, 7, 2, 48, 18, 9, 3, 55, 21, 11, 4, 63, 24, 12, 6, 71, 27, 14, 7, 1, 80, 30, 16, 8, 2, 89, 34, 18, 9, 3, 99, 37, 20, 11, 4, 109, 41, 22, 13, 5, 120, 45, 24, 14, 7, 131, 49, 27, 15, 8, 1, 143, 53, 29, 17, 9, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column k lists the partial sums of the k-th column of triangle A237591.

We can see this sequence in the front view of the pyramid described in A245092.

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

Triangle begins:

    1;

    3;

    5,  1;

    8,  2;

   11,  4;

   15,  5,  1;

   19,  7,  2;

   24,  9,  3;

   29, 11,  5;

   35, 13,  6,  1;

   41, 16,  7,  2;

   48, 18,  9,  3;

   55, 21, 11,  4;

   63, 24, 12,  6;

   71, 27, 14,  7,  1;

   80, 30, 16,  8,  2;

   89, 34, 18,  9,  3;

   99, 37, 20, 11,  4;

  109, 41, 22, 13,  5;

  120, 45, 24, 14,  7;

  131, 49, 27, 15,  8,  1;

...

Illustration for n = 10:

We draw the first 10 rows of the infinite diagram described in A237591 as shown below:

Row                           _

1                           _| |

2                         _|  _|

3                       _|   | |

4                     _|    _| |

5                   _|     |  _|

6                 _|      _| | |

7               _|       |   | |

8             _|        _|  _| |

9           _|         |   |  _|

10         |_ _ _ _ _ _|_ _|_|_|

Area             35     13  6 1

.

The diagram contains four regions and the areas of the successives regions from left to right are respectively [35, 13, 6, 1], so the 10th row of this triangle is [35, 13, 6, 1].

Note that this infinite diagram gives a correspondence between the number of partitions into k consecutive parts and the symmetric representation of A000203, A024916, A004125 and many other integer sequences. For more information see A196020, A236104, A235791, A237048, A237593, A262626, A286000 and A286001.

CROSSREFS

Row n has length A003056(n) hence column k starts in row A000217(k).

Row sums give A000217, n >= 1.

Column 1 gives A024206 without its initial zero.

Column 2 gives the partial sums of the A261348.

Cf. A000203, A004125, A024916, A196020, A235791, A236104, A237048, A237591, A237593, A244050, A245092, A262626, A286000, A286001.

Sequence in context: A242390 A065395 A236631 * A340529 A197326 A235605

Adjacent sequences:  A302797 A302798 A302799 * A302801 A302802 A302803

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 13 2018

STATUS

approved

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Last modified January 17 22:33 EST 2022. Contains 350410 sequences. (Running on oeis4.)