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 A118141 #14 Mar 08 2015 18:40:13 %S A118141 2,3,5,4,23,8,11,27,29,30,47,62,17,339,23,254,167,512,59,2339,185, %T A118141 2046,95,1024,125,2043,35,3276,2039,340,47,4091,509,4094,335,3590, %U A118141 1025,16379,119,1048574,4679,16382,371,92819,12281,8388606,191,2097152,6149,262139 %N A118141 Length of the longest perfect parity pattern with n columns. %C A118141 Also the length of the unique perfect parity pattern whose first row is 0....01 (with n-1 zeros). %C A118141 Definitions: A parity pattern is a matrix of 0's and 1's with the property that every 0 is adjacent to an even number of 1's and every 1 is adjacent to an odd number of 1's. %C A118141 It is called perfect if no row or column is entirely zero. Every parity pattern can be built up in a straightforward way from the smallest perfect subpattern in its upper left corner. %C A118141 For example, the 3 X 2 matrix %C A118141 11 %C A118141 00 %C A118141 11 %C A118141 is a parity pattern built up from the perfect 1 X 2 pattern "11". The 3 X 5 matrix %C A118141 01010 %C A118141 11011 %C A118141 01010 %C A118141 is similarly built up from the perfect 3 X 2 pattern of its first two columns. The 4 X 4 matrix %C A118141 0011 %C A118141 0100 %C A118141 1101 %C A118141 0101 %C A118141 is perfect. So is the 5 X 5 %C A118141 01110 %C A118141 10101 %C A118141 11011 %C A118141 10101 %C A118141 01110 %C A118141 which moreover has 8-fold symmetry (cf. A118143). %C A118141 All perfect parity patterns of n columns can be shown to have length d-1 where d divides a(n)+1. %D A118141 D. E. Knuth, The Art of Computer Programming, Section 7.1.3. %H A118141 Andries E. Brouwer, Jun 15 2008, <a href="/A118141/b118141.txt">Table of n, a(n) for n = 1..85</a> %H A118141 Andries E. Brouwer, <a href="http://www.win.tue.nl/~aeb/ca/madness/madrect.html">Button Madness and Lights Out on rectangles</a> %Y A118141 The number of perfect parity patterns that have exactly n columns is A000740. %Y A118141 The sequence of all n such that an n X n parity pattern exists is A117870 (cf. A076436, A093614, A094425). %Y A118141 Cf. also A118142, A118143. %Y A118141 Cf. A007802. %K A118141 nonn %O A118141 1,1 %A A118141 _Don Knuth_, May 11 2006 %E A118141 More terms from _John W. Layman_, May 17 2006 %E A118141 More terms from _Andries E. Brouwer_, Jun 15 2008