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

1,4

Comments

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

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

Table of n, a(n) for n=1..83.

Peter Luschny, Integer Partition Trees, OEIS wiki.

Example

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]]

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.

Sequence in context: A193073 A228100 A211992 * A340035 A185147 A206921

Adjacent sequences: A182934 A182935 A182936 * A182938 A182939 A182940

Keyword

nonn,tabf

Author

Peter Luschny, Jan 21 2011

Status

approved