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A186412 Sum of all parts in the n-th region of the set of partitions of j, if 1<=n<=A000041(j). 30
1, 3, 5, 2, 9, 3, 12, 2, 6, 3, 20, 3, 7, 4, 25, 2, 6, 3, 13, 5, 4, 38, 3, 7, 4, 14, 3, 9, 5, 49, 2, 6, 3, 13, 5, 4, 23, 4, 10, 6, 5, 69, 3, 7, 4, 14, 3, 9, 5, 27, 5, 4, 15, 7, 6, 87, 2, 6, 3, 13, 5, 4, 23, 4, 10, 6, 5, 39, 3, 9, 5, 19, 4, 12, 7, 6, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also triangle read by rows: T(j,k) = sum of all parts in the k-th region of the last section of the set of partitions of j. See Example section. For more information see A135010. - Omar E. Pol, Nov 26 2011

For the definition of "region" see A206437. - Omar E. Pol, Aug 19 2013

LINKS

Table of n, a(n) for n=1..77.

FORMULA

a(A000041(n)) = A046746(n).

EXAMPLE

Contribution from Omar E. Pol, Nov 26 2011 (Start):

Written as a triangle:

1;

3;

5;

2,9;

3,12;

2,6,3,20;

3,7,4,25;

2,6,3,13,5,4,38;

3,7,4,14,3,9,5,49;

2,6,3,13,5,4,23,4,10,6,5,69;

3,7,4,14,3,9,5,27,5,4,15,7,6,87;

2,6,3,13,5,4,23,4,10,6,5,39,3,9,5,19,4,12,7,6,123;

(End)

From Omar E. Pol, Aug 18 2013: (Start)

Illustration of initial terms (first seven regions):

.                                             _ _ _ _ _

.                                     _ _ _  |_ _ _ _ _|

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

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

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

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

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

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

.

.   1     3       5     2         9       3          12

.

(End)

CROSSREFS

Row sums of triangle A186114 and of triangle A193870.

Row j has length A187219(j).

Row sums give A138879.

Right border gives A046746, j >= 1.

Records give A046746, j >= 1.

Partial sums give A182244.

Cf. A000041, A002865, A066186, A135010, A138121, A138879, A194436, A194437, A194438, A194439, A194446, A194447.

Sequence in context: A026143 A075626 A152649 * A322982 A275846 A273668

Adjacent sequences:  A186409 A186410 A186411 * A186413 A186414 A186415

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 12 2011

STATUS

approved

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Last modified October 14 17:31 EDT 2019. Contains 328022 sequences. (Running on oeis4.)