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.
%I A229161 #42 Apr 15 2016 14:32:30 %S A229161 0,1,1,2,5,13,42,155,636,2889,14321,76834,443157 %N A229161 Number of n X n binary matrices with exactly 2 ones in each row and column, and with rows and columns in lexicographically nondecreasing order. %C A229161 A column of A227061. %C A229161 From _Brendan McKay_, Sep 16 2013: (Start) %C A229161 If all row and column permutations are allowed, one gets A002865 for k=2, A000512 for k=3, A000513 for k=4, A000516 for k=5, etc., where k = number of 1's in each row and column. See also A133687. %C A229161 A229161 is strictly different from A002865, which gives the number of equivalence classes of n X n binary matrices with exactly 2 1's in each row and column, up to permutations of rows and columns. %C A229161 For example, take two non-equivalent n X n matrices A,B which are in sorted form (i.e. the rows are in increasing order and so are the columns). Now form a 2n X 2n matrix by placing A and B in the off-diagonal blocks and zeros in the two diagonal blocks. This matrix is in sorted form. Interchanging A and B gives a different matrix that is also in sorted form, and yet it is easily produced from the first matrix by permuting rows and columns. That is, one equivalence class can contain two different sorted matrices. I expect that on average the number of sorted matrices per equivalence class is exponentially large. %C A229161 (End) %D A229161 K. Yordzhev, On an Algorithm for Isomorphism-Free Generations of Combinatorial Objects, International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Web Site: www.ijettcs.org, Volume 2, Issue 6, November - December 2013, ISSN 2278-6856 %H A229161 K. Yordzhev, <a href="http://arXiv.org/abs/1305.6790">Fibonacci sequence related to a combinatorial problem on binary matrices</a>, arXiv preprint arXiv:1305.6790, 2013 %H A229161 K. Yordzhev, <a href="http://arxiv.org/abs/1506.04642">Semi-canonical binary matrices</a>, arXiv preprint arXiv:1506.04642, 2015 %Y A229161 Cf. A229162, A229163, A229164, A181344, A181345, A002865, A000512, A000513, A000516, A133687. %K A229161 nonn,more %O A229161 1,4 %A A229161 _N. J. A. Sloane_, Sep 15 2013 %E A229161 Better definition and values of a(12)-a(13) from _R. H. Hardin_, Sep 17 2013