A330644 Number of non-self-conjugate partitions of n.

0, 0, 2, 2, 4, 6, 10, 14, 20, 28, 40, 54, 74, 98, 132, 172, 226, 292, 380, 484, 620, 784, 994, 1246, 1564, 1946, 2424, 2996, 3702, 4548, 5586, 6822, 8326, 10118, 12284, 14854, 17944, 21602, 25978, 31144, 37292, 44534, 53122, 63204, 75112, 89066, 105486, 124676, 147186, 173432

Offset

0,3

Comments

Also number of asymmetric Ferrers graphs with n nodes.

Links

Table of n, a(n) for n=0..49.

Formula

a(n) = A000041(n) - A000700(n).

a(n) = 2*A000701(n).

Example

For n = 5 the partitions of 5 and their respective Ferrers graphs are as follows:
.
  5 * * * * *    4 * * * *    3 * * *    3 * * *    2 * *    2 * *    1 *
                 1 *          2 * *      1 *        2 * *    1 *      1 *
                                         1 *        1 *      1 *      1 *
                                                             1 *      1 *
                                                                      1 *
The number 5 has seven partitions, and one of them [3, 1, 1] is a self-conjugate partition, hence the number of non-self-conjugate partitions of 5 is 7 - 1 = 6, so a(5) = 6.
On the other hand there are six asymmetric Ferrers graphs with n nodes, they are the graphs associated to the partitions [5], [4, 1], [3, 2], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1], so a(5) = 6.

Crossrefs

Cf. A000041, A000700, A000701, A046682.

Sequence in context: A098330 A240310 A083848 * A278297 A139582 A300415

Adjacent sequences: A330641 A330642 A330643 * A330645 A330646 A330647

Keyword

nonn

Author

Omar E. Pol, Jan 10 2020

Status

approved