A208479 Total sum of the numbers of partitions with positive k-th ranks of all partitions of n.

0, 2, 3, 6, 10, 18, 27, 45, 65, 99, 141, 206, 285, 403, 549, 754, 1011, 1364, 1800, 2388, 3116, 4072, 5257, 6791, 8678, 11093, 14058, 17800, 22380, 28111, 35087, 43748, 54256, 67189, 82831, 101962, 124997, 153011, 186632, 227281, 275905, 334418, 404159, 487714

Offset

1,2

Comments

For the definition of k-th rank see A208478.

Links

Table of n, a(n) for n=1..44.

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 number of partitions of 4 with positive k-th ranks are 2, 1, 2, 1 so the total sum is a(4) = 2+1+2+1 = 6.

Crossrefs

Row sums of A208478.

Cf. A208482, A208483.

Sequence in context: A026779 A081028 A325232 * A065441 A075531 A066067

Adjacent sequences: A208476 A208477 A208478 * A208480 A208481 A208482

Keyword

nonn

Author

Omar E. Pol, Mar 07 2012

Extensions

More terms from Alois P. Heinz, Mar 11 2012

Status

approved