A208483 Total sum of the sums of all positive k-th ranks of all partitions of n.

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

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