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

Author

Omar E. Pol, Jan 10 2020

Keywords

• nonn

Comments

Also number of asymmetric Ferrers graphs with n nodes.

Examples

			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.

Formula

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

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