A176210 Triangle read by rows in which row n (n>=3) lists those partitions of n with every part > 2.

3, 4, 5, 6, 3, 3, 7, 4, 3, 8, 5, 3, 4, 4, 9, 6, 3, 5, 4, 3, 3, 3, 10, 7, 3, 6, 4, 5, 5, 4, 3, 3, 11, 8, 3, 7, 4, 6, 5, 5, 3, 3, 4, 4, 3, 12, 9, 3, 8, 4, 7, 5, 6, 6, 6, 3, 3, 5, 4, 3, 4, 4, 4, 3, 3, 3, 3, 13, 10, 3, 9, 4, 8, 5, 7, 6, 7, 3, 3, 6, 4, 3, 5, 5, 3, 5, 4, 4, 4, 3, 3, 3

Offset

3,1

Comments

Each partition is listed in nonincreasing order.

The partitions in each row are listed in decreasing lexicographic order.

Also the numbers of vertices of the connected components of the 2-regular simple graphs on n vertices.

Links

J. S. Kimberley, Rows 3..39 of A176210 triangle, flattened [b-file corrected by N. J. A. Sloane, Oct 05 2010]

Example

For n in {0,1,2} there are no parts; so those rows are empty.
3 (one partition only)
4 (one partition only)
5 (one partition only)
6; 3, 3
7; 4, 3
8; 5, 3; 4, 4
9; 6, 3; 5, 4; 3, 3, 3
10; 7, 3; 6, 4; 5, 5; 4, 3, 3
11; 8, 3; 7, 4; 6, 5; 5, 3, 3; 4, 4, 3
12; 9, 3; 8, 4; 7, 5; 6, 6; 6, 3, 3; 5, 4, 3; 4, 4, 4; 3, 3, 3, 3
13; 10, 3; 9, 4; 8, 5; 7, 6; 7, 3, 3; 6, 4, 3; 5, 5, 3; 5, 4, 4; 4, 3, 3, 3

Prog

(Magma) &cat[ &cat RestrictedPartitions(n, {3..n}):n in [1..13]];

Crossrefs

The number of partitions in each row is A008483.

The length of each row is A177739.

The same ordering is used in A080577 and A138136 (for other orderings see A036036 and A036037).

Sequence in context: A185383 A004484 A332882 * A187824 A357081 A177028

Adjacent sequences: A176207 A176208 A176209 * A176211 A176212 A176213

Keyword

easy,nonn,tabf

Author

Vladimir Shevelev, Apr 12 2010

Extensions

Extensively edited by Jason Kimberley, May 13 2010

Status

approved