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A208479 Total sum of the numbers of partitions with positive k-th ranks of all partitions of n. 6
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 (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..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

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)