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A208482 Triangle read by rows: T(n,k) = sum of positive k-th ranks of all partitions of n. 6
0, 1, 1, 2, 1, 1, 4, 1, 2, 1, 7, 1, 3, 2, 1, 12, 2, 5, 4, 2, 1, 18, 3, 6, 6, 4, 2, 1, 29, 6, 9, 10, 7, 4, 2, 1, 42, 9, 11, 13, 11, 7, 4, 2, 1, 63, 16, 15, 19, 17, 12, 7, 4, 2, 1, 89, 24, 18, 25, 24, 18, 12, 7, 4, 2, 1, 128, 39, 24, 36, 34, 28, 19, 12, 7, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For the definition of the k-th rank see A208478.

It appears that the sum of the k-th ranks of all partitions of n is equal to zero.

It appears that reversed rows converge to A000070, the same as A208478. - Omar E. Pol, Mar 10 2012

LINKS

Alois P. Heinz, Rows n = 1..44, flattened

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 row 4 lists 4, 1, 2, 1.

Triangle begins:

0;

1,    1;

2,    1,  1;

4,    1,  2,  1;

7,    1,  3,  2,  1;

12,   2,  5,  4,  2,  1;

18,   3,  6,  6,  4,  2,  1;

29,   6,  9, 10,  7,  4,  2,  1;

42,   9, 11, 13, 11,  7,  4,  2,  1;

63,  16, 15, 19, 17, 12,  7,  4,  2,  1;

89,  24, 18, 25, 24, 18, 12,  7,  4,  2,  1;

128, 39, 24, 36, 34, 28, 19, 12,  7,  4,  2,  1;

CROSSREFS

Column 1 is A209616. Row sums give A208483.

Cf. A006128, A063995, A064173, A105805, A181187, A194547, A194549, A195822, A208478.

Sequence in context: A105477 A325772 A226174 * A199856 A301906 A302150

Adjacent sequences:  A208479 A208480 A208481 * A208483 A208484 A208485

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Mar 07 2012

EXTENSIONS

Terms a(1)-a(22) confirmed and additional terms added by John W. Layman, Mar 10 2012

STATUS

approved

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Last modified September 15 12:44 EDT 2019. Contains 327078 sequences. (Running on oeis4.)