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A208483 Total sum of the sums of all positive k-th ranks of all partitions of n. 7
0, 2, 4, 8, 14, 26, 40, 68, 100, 156, 224, 334, 466, 668, 920, 1278, 1726, 2356, 3130, 4190, 5508, 7254, 9422, 12268, 15764, 20284, 25852, 32934, 41616, 52578, 65938, 82648, 102976, 128144, 158660, 196222, 241534, 296946, 363632, 444650, 541794, 659268, 799606 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the definition of k-th rank see A208478.

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

For n = 4 the partitions of 4 and the four types of ranks of the partitions of 4 are

----------------------------------------------------------

Partitions    First      Second       Third      Fourth

of 4          rank        rank        rank        rank

----------------------------------------------------------

4           4-1 =  3    0-1 = -1    0-1 = -1    0-1 = -1

3+1         3-2 =  1    1-1 =  0    0-1 = -1    0-0 =  0

2+2         2-2 =  0    2-2 =  0    0-0 =  0    0-0 =  0

2+1+1       2-3 = -1    1-1 =  0    1-0 =  1    0-0 =  0

1+1+1+1     1-4 = -3    1-0 =  1    1-0 =  1    1-0 =  1

----------------------------------------------------------

The sums of positive k-th ranks of the partitions of 4 are 4, 1, 2, 1 so the total sum is a(4) = 4+1+2+1 = 8.

CROSSREFS

Row sums of triangle A208482.

Cf. A208478, A208479.

Sequence in context: A164148 A065492 A298880 * A284735 A006777 A036609

Adjacent sequences:  A208480 A208481 A208482 * A208484 A208485 A208486

KEYWORD

nonn

AUTHOR

Omar E. Pol, Mar 07 2012

EXTENSIONS

More terms from Alois P. Heinz, Mar 11 2012

STATUS

approved

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)