A182937 Triangle in which n-th row lists all integer partitions of n, in order of traversing the periphery of the Fenner-Loizou tree in the clockwise sense.

1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 4, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 4, 1, 5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 5, 1, 6, 4, 2, 3, 2, 1, 3, 3, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Peter Luschny, Jan 21 2011

Keywords

• nonn
• tabf

Comments

If the Fenner-Loizou tree is traversed in the counterclockwise sense (preorder traversal) the integer partitions are in lexicographic order.

Examples

			First five rows are:
[[1]]
[[1, 1], [2]]
[[1, 1, 1], [2, 1], [3]]
[[1, 1, 1, 1], [2, 1, 1], [3, 1], [4], [2, 2]]
[[1, 1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 1], [4, 1], [5], [3, 2], [2, 2,1]]
		

References

• T. I. Fenner and G. Loizou, Comp. J. 23 (1980), 332-337.
• D. E. Knuth, TAOCP 4 (2005), fasc. 3, 7.2.1.4, exercise 10.

Links

• Peter Luschny, Integer Partition Trees, OEIS wiki.

Crossrefs

See A036036 for the Hindenburg (graded reflected colexicographic) ordering.

See A036037 for the graded colexicographic ordering.

See A080576 for the Maple (graded reflected lexicographic) ordering.

See A080577 for the Mathematica (graded reverse lexicographic) ordering.

See A193073 for the graded lexicographic ordering.

See A228100 for the Fenner-Loizou (binary tree) ordering.