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 A094858 #2 Feb 27 2009 03:00:00 %S A094858 1,2,2,4,4,6,8,11,15,20,26,36,51 %N A094858 Maximal number of longest common subsequences between any two binary strings of length n (Version 2). %C A094858 Definitions: S is a subsequence of X if S can be obtained by deleting some (not necessarily adjacent) entries of X. %C A094858 S is a longest common subsequence of X and Y if S is a subsequence of X, S is a subsequence of Y and for any T, if T is a subsequence of X and of Y, then |T| <= |S|. Let LCS(X,Y) = length of any longest common subsequence of X and Y. %C A094858 For each common subsequence S of X and Y, there may be several ways to delete entries from X and from Y to get S, but in this version of the problem we do not take this into account (cf. A094837). Let F(X,Y) be the number of different choices for S, without regard to where it appears in X and Y. Sequence gives max F(X,Y) over all choices for binary strings X and Y of length n. %C A094858 For this version of the problem using a larger alphabet helps (cf. A094859, A094863). %C A094858 For an alphabet of size m = 2, 3 or 4, the maximum appears to be attained for X=123..m123..m..., except for some small values of n. For m>4 it seems that only 4 letters should be chosen in X,Y to get the maximum, while the other letters are ignored. %C A094858 Hill-climbing gives the following lower bounds for the next few terms: 26,36,50,70,96,141,192. %Y A094858 Cf. A094859-A094862, A094837, A094824, A094291. %K A094858 nonn,nice,more %O A094858 1,2 %A A094858 Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004