cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A330644 #16 Jan 10 2020 13:17:40
%S A330644 0,0,2,2,4,6,10,14,20,28,40,54,74,98,132,172,226,292,380,484,620,784,
%T A330644 994,1246,1564,1946,2424,2996,3702,4548,5586,6822,8326,10118,12284,
%U A330644 14854,17944,21602,25978,31144,37292,44534,53122,63204,75112,89066,105486,124676,147186,173432
%N A330644 Number of non-self-conjugate partitions of n.
%C A330644 Also number of asymmetric Ferrers graphs with n nodes.
%F A330644 a(n) = A000041(n) - A000700(n).
%F A330644 a(n) = 2*A000701(n).
%e A330644 For n = 5 the partitions of 5 and their respective Ferrers graphs are as follows:
%e A330644 .
%e A330644   5 * * * * *    4 * * * *    3 * * *    3 * * *    2 * *    2 * *    1 *
%e A330644                  1 *          2 * *      1 *        2 * *    1 *      1 *
%e A330644                                          1 *        1 *      1 *      1 *
%e A330644                                                              1 *      1 *
%e A330644                                                                       1 *
%e A330644 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.
%e A330644 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.
%Y A330644 Cf. A000041, A000700, A000701, A046682.
%K A330644 nonn
%O A330644 0,3
%A A330644 _Omar E. Pol_, Jan 10 2020