A302800 - OEIS

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.

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:

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 * A367067 A340529 A197326

Adjacent sequences: A302797 A302798 A302799 * A302801 A302802 A302803

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 13 2018

STATUS

approved