OFFSET
1,2
COMMENTS
EXAMPLE
First 8 rows:
1
2 0
3 1 1
4 2 0 2 0
5 3 1 3 1 1 1
6 4 2 4 0 2 2 2 0 2 0
7 5 3 5 1 3 3 1 3 1 3 1 1 1 1
8 6 4 6 2 4 4 0 2 4 2 4 2 0 2 2 2 0 2 0 2 0
Row 5 comes from arranging the 7 partitions of 5 is this order:
[5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1] and taking alternating sums: 5, 4-1, 3-1, 3-1+1, 2-2+1, 2-1+1-1, 1-1+1-1.
MATHEMATICA
r[n_] := Map[Total[Map[Total, {Take[##], Drop[##]} &[#, {1, -1, 2}] {1, -1}]] &, IntegerPartitions[n]]; Column[Table[r[n], {n, 10}]] (* Peter J. C. Moses, May 15 2019 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, May 17 2019
STATUS
approved