OFFSET

1,4

COMMENTS

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

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